Measuring and modelling the isotopic composition of soil respiration : insights from a grassland tracer experiment

Introduction Conclusions References


Introduction
The carbon isotopic composition (δ 13 C) of soil respiration is often interpreted in terms of environmental and metabolic effects on soil carbon dynamics (e.g., McDowell et al., 2004;Ekblad et al., 2005;Mortazavi et al., 2005;Bahn et al., 2009;Gavrichkova et al., 2011;Salmon et al., 2011;Werner and Gessler, 2011).In general, δ 13 C of the respiratory source (δ 13 C Rs ) is not measured directly, but is equated with δ 13 C of CO 2 efflux (δ 13 C efflux ).However, soil CO 2 efflux can differ isotopically from concurrent respiratory CO 2 production due to transient conditions within the soil CO 2 pool.This divergence (termed "disequilibrium effect" in the following) complicates the interpretation of δ 13 C Rs .Here we investigate mechanisms affecting this disequilibrium effect.
Transient conditions in the soil diffusive system have been observed under natural conditions (e.g., Dudziak and Halas, 1996;Millard et al., 2008;Maseyk et al., 2009;Moyes et al., 2010), but may be particularly evident following tracer application.For instance, Staddon et al. (2003) and Leake et al.U. Gamnitzer et al.: Isotopic composition of soil respiration (2006) noted a diffusion of CO 2 tracer into the soil during pulse-labelling experiments and mentioned this as a potential source of error for estimates of δ 13 C Rs .Indeed, Subke et al. (2009) used a diffusion model to show that 13 CO 2 pulselabelling of atmospheric CO 2 led to a change in the δ 13 C of CO 2 in soil pores, due to transfer of the tracer into the soil pore space.Back-diffusion of the tracer into the atmosphere after labelling was thought to cause an abiotic tracer flux (non-biological tracer flux from the soil into the overlying atmosphere, due to physical processes rather than to respiration of previously assimilated labelled carbon) for up to 2 d after tracer application.Recently, Ohlsson (2011) investigated δ 13 C efflux in the dataset of Subke et al. with a diffusion model, which was designed to simulate pulse labelling experiments.To our knowledge, this is the only study quantifying the effects of tracer application and associated changes in δ 13 C in soil pore CO 2 on δ 13 C efflux in a mechanistic way.
In addition to the soil air pores, Högberg et al. (2008) suggested that isotopically labelled CO 2 would also dissolve in soil water.The amount of CO 2 dissolved in water (more precisely the sum of dissolved CO 2 , carbonic acid, bicarbonate and carbonate) can be several times higher than the amount of CO 2 in the same volume of air.Thus, transient conditions in dissolved CO 2 will likely increase the abiotic tracer flux compared to conditions where dissolution in water is not important, as predicted by Ohlsson (2011).The extent of the contribution from the dissolved CO 2 storage pool depends on the equilibration time between CO 2 in the gaseous and dissolved phase: when this equilibration occurs quickly compared to the residence time of CO 2 in soil air pores, then the total soil CO 2 pool (gaseous+dissolved CO 2 ) is expected to influence δ 13 C efflux by prolonging the disequilibrium.Despite the potential of dissolution to affect δ 13 C efflux , a quantitative investigation of this effect is limited to a single study (Ohlsson, 2011).
Another mechanism influencing soil CO 2 efflux is advective transport by bulk fluid flow (rather than diffusion).Camarda et al. (2007) and Kayler et al. (2010b) investigated δ 13 C of CO 2 in soil air pores and δ 13 C efflux in advectivediffusive regimes.Bowling et al. (2009) illustrated that the δ 13 C in CO 2 within a snowpack depends on the physical nature of the transport mechanism, an analogous dependency may occur for CO 2 in soil pores.Advection is also expected to transfer an atmospheric tracer signal into soil air.Advective transport has been described to occur due to chamber artifacts (e.g., Kanemasu et al., 1974;Fang and Moncrieff, 1998;Lund et al., 1999;Davidson et al., 2002;Pumpanen et al., 2004).Even small pressure differences between the inside and outside of chambers, in the order of 1 Pa, have been shown to considerably influence the soil CO 2 efflux (Fang and Moncrieff, 1998;Lund et al., 1999).Phillips et al. (2010) found indications that advection introduced by sampling affected estimations of δ 13 C Rs .
Disequilibrium effects can occur in all systems where the diffusive flux profile varies over time.For example, iso-topic disequilibrium can be caused by introduction of an isotopic tracer via 13 CO 2 (Ostle et al., 2000;Carbone and Trumbore, 2007;Högberg et al., 2008;Subke et al., 2009) or 14 CO 2 (Horwath et al., 1994;Carbone et al., 2007) pulse labelling, or in Free-Air CO 2 Enrichment (FACE and web-FACE) experiments (e.g., Nitschelm et al., 1997;Matamala et al., 2003;Asshoff et al., 2006;Keel et al., 2006;Pregitzer et al., 2006;Taneva et al., 2006).Epron et al. (2011) used a crown chamber for 13 CO 2 labelling of trees to prevent tracer diffusion into soil pores.Similarly, changes in chamber headspace CO 2 due to flushing with CO 2 -free air can affect the measurement of δ 13 C efflux (Ohlsson et al., 2005).Transient conditions in diffusive flux profiles in the soil of natural (unlabelled) systems can be caused by time-varying respiratory CO 2 production (Moyes et al., 2010).Some complications in the interpretation of diffusive flux profiles were discussed by Koehler et al. (2010).From a diffusion experiment involving artificial soil and CO 2 source, Kayler et al. (2008) concluded that non-steady-state effects must be considered in field investigations of δ 13 C Rs in soils.Furthermore, Kayler et al. (2010b) demonstrated in a field study the interrelation between perturbations of CO 2 in soil pores and aboveground measurement techniques for δ 13 C of soil respiration.Numerical approaches considering diffusion of CO 2 in soil air have been applied to simulate the impact of transient changes in environmental variables (Nickerson and Risk, 2009a;Moyes et al., 2010) or the deployment of respiration chambers (Nickerson and Risk, 2009b,c;Ohlsson, 2010) on δ 13 C efflux and, again, the disequilibrium effect.For example, CO 2 accumulating in the headspace of closed chambers and associated chamber-soil feedbacks can cause deviation of Keeling plots (Keeling, 1958) from linearity (Nickerson and Risk, 2009b;Kammer et al., 2011).For various soil respiration chambers, Nickerson and Risk (2009c) predicted disequilibrium effects mostly ranging around several permil, with a maximum of 15 ‰.The return to equilibrium takes longer if CO 2 in soil air pores exchanges with CO 2 dissolved in soil water.Accordingly, for a given sampling scheme with fixed sampling times (e.g.Keeling plots), the system deviates stronger from equilibrium when dissolved CO 2 is involved in soil gas transport.Thus, the divergence of δ 13 C efflux from δ 13 C Rs captured by sampling is expected to be even larger than predicted by Nickerson and Risk.Soil respiration accounts for a major fraction of grassland ecosystem respiration, thus disequilibrium effects in soils can generally affect the interpretation of the isotopic signal of grassland ecosystem respiration.Shoot respiration (the remaining fraction of ecosystem respiration) is not expected to produce comparable disequilibrium effects for carbon isotopes, since the relatively small CO 2 pool in leaf intercellular space is turned over much faster than the soil CO 2 pool.
Here, we investigate the disequilibrium effect in ecosystem respiration in a field labelling experiment.In that experiment, a grassland ecosystem was exposed during daytime Biogeosciences, 8, 1333Biogeosciences, 8, -1350Biogeosciences, 8, , 2011 www.biogeosciences.net/8/1333/2011/ to CO 2 with a δ 13 C of −46.9 ‰ for 2 weeks (Gamnitzer et al., 2009).Nocturnal δ 13 C efflux of the ecosystem was measured with three independent methods: steady-state open chambers, closed chambers (both in-situ in the field), and laboratory-based cuvettes with excised soil + vegetation blocks.The δ 13 C efflux data of the open chamber measurements agreed with those of the cuvette measurements (Gamnitzer et al., 2009).This indicated that the δ 13 C efflux of the open chamber measurements gave an accurate estimate of δ 13 C Rs .In consequence, we used the open chamber data as "true" δ 13 C Rs in the following.
The closed chamber measurements employed a Keeling plot approach.These estimates of ecosystem δ 13 C efflux deviated by ∼10 ‰ from δ 13 C Rs .We suspected that this discrepancy was associated with a disequilibrium effect.Thus, the aim of the present work is to quantify the impact of mechanisms which could underlie such a disequilibrium effect between δ 13 C Rs and δ 13 C efflux .In particular, we investigated effects of diffusion of CO 2 in soil gas, dissolution of CO 2 in soil water, and advection of soil gas due to chamber pressurization during labelling.For this purpose, we present a new soil CO 2 transport model which accounts for respiratory CO 2 production, diffusion, dissolution, and advection of both 12 CO 2 and 13 CO 2 .We applied the soil CO 2 transport model to evaluate the mechanism(s) underlying abioticallydriven flux of tracer.We simulated the labelling experiment and predicted Keeling plot intercepts for nocturnal CO 2 accumulation in the closed chambers with the model.Simulation results were compared to observations to assess the quantitative importance of the different mechanisms underlying the disequilibrium effect.Lastly, we discuss the consequences of these mechanisms for commonly used isotopic approaches for the study of soil and ecosystem respiration.

Soil CO 2 transport model
The transport of CO 2 in soil pore spaces and exchange with the overlying atmosphere was simulated using a vertical (one-dimensional) soil CO 2 transport model, which also included an aboveground (shoot) respiration component.Isotopologues of CO 2 were treated as separate gases using a separate set of equations for each.The total CO 2 concentration ( 12 CO 2 + 13 CO 2 ) and the δ 13 C of CO 2 (δ 13 C = R sample /R standard − 1, where R sample and R standard are the 13 C/ 12 C ratios in the sample and in the international VPDB standard) were calculated from modelled 12 CO 2 and 13 CO 2 .The model was based on the following mass balance equation ( Šimůnek and Suarez, 1993;Fang and Moncrieff, 1999): J diff and J adv describe the CO 2 fluxes (µmol m −2 s −1 ) caused by diffusion in the gas phase and by advection of soil air, respectively.P Rs represents the total CO 2 production (µmol m −3 s −1 ) by the respiratory source, including belowground and aboveground respiration.t denotes the time (s) and z the depth (m) below the soil surface.c T is the total CO 2 concentration (molar concentration; µmol m −3 ) in both the gas and liquid phases and is given by where c a and c w are the CO 2 concentrations (µmol m −3 ) in the gas and dissolved phase.Conversion between CO 2 concentration c a (µmol m −3 ) and CO 2 mole fraction C (µmol mol −1 ) followed c a = C/V mol , where V mol is the molar volume of an ideal gas (22.4 L mol −1 at standard conditions; adapted to site conditions for temperature and pressure).ε a and ε w denoted the volumetric fractions (m 3 m −3 ) of air and water in the soil.The total (air-filled + water-filled) porosity of the soil, ε tot (m 3 m −3 ), is given by The total amount of carbon in the dissolved phase was calculated according to Wood et al. (1993) as the sum of H 2 CO 3 (aq) (which summarises CO 2 (aq) and H 2 CO 3 , as is commonly used) and HCO − 3 (bicarbonate).Thus, where the square brackets indicate concentrations.H 2 CO 3 (aq) and HCO − 3 represent 99.9 % of the dissolved carbon species in the pH range at our study site (pH ∼ 7.5, see Table 1).Thus, CO 2− 3 was neglected.The chemical equilibrium reactions and constants can be expressed as (e.g., Stumm and Morgan, 1996) CO 2 (g) These allow the calculation of the concentrations [H 2 CO 3 (aq)] and [HCO − 3 ] (mol L −1 ) when p CO 2 , the CO 2 partial pressure (kPa), and the pH are known.p CO 2 was derived from p CO 2 =RT c a , where R is the universal gas constant (8.314 kg m 2 s −2 K −1 mol −1 ) and T the temperature (K).According to Eqs. ( 4)-( 6), the so-called Bunsen coefficient B = c w /c a is given by Numerical values for K H , the Henry's law constant, and the equilibrium constant K 1 were taken from Stumm and Morgan (1996).Fractionation for the dissolution of CO 2 in water was included according to Mook et al. (1974)  Determined according to Eq. ( 11) from observed pressure difference (Gamnitzer et al., 2009) and assumed air permeability of the soil of 10.1 (4.85-52.5)µm 2 (median and 25 %-75 % quantil; Ball et al., 1997;Fish and Koppi, 1994;Milne and Haynes, 2004;Munkholm et al., 2005;Schjønning et al., 2007) Diffusivity model: D soil /D 0 0.030 (0.014-0.18)Millington (1959); Millington and Quirk (1960); Moldrup et al. (1997Moldrup et al. ( , 1999Moldrup et al. ( , 2000Moldrup et al. ( , 2004) ) H 2 CO 3 (aq) by (9866/T −24.12) ‰, see Mook (2000).This description of dissolution of CO 2 in soil water implies instantaneous equilibration between the gaseous and the dissolved phase.
The CO 2 fluxes were defined by D soil is the diffusion coefficient for CO 2 in soil air (m 2 s −1 ), and v Darcy is the Darcy velocity (m s −1 ).Equation ( 8) corresponds to Fick's First Law.D soil was derived from D 0 , the diffusion coefficient (m 2 s −1 ) for CO 2 in air, according to Millington (1959), D 0 was derived for the average soil temperature during the field experiment following Fuller et al. (1966) (see also Campbell and Norman, 1998).Further estimates of (effective) soil diffusivity (Millington and Quirk, 1960;Moldrup et al., 1997Moldrup et al., , 1999Moldrup et al., , 2000Moldrup et al., , 2004) ) were used to investigate sensitivity to the choice of a D soil model.Fractionation during diffusion was taken into account by applying different diffusivities for the isotopologues (Cerling et al., 1991): D soil ( 12 CO 2 )/D soil ( 13 CO 2 )=1.0044.The Darcy velocity was derived from Darcy's law, where k a is the air permeability of the soil, η a the dynamic viscosity of air, and p the pressure difference occuring over the distance z.
For numerical solution of Eq. ( 1), the soil was divided into n horizontal layers of thickness z = L/n, where L is the total soil depth.An additional top layer (depth 0) represented the atmosphere above the soil.The CO 2 production by the respiratory source, P Rs , corresponded to belowground (soil) respiration in the soil layers, and to aboveground (shoot) respiration in the top (atmospheric) layer.While the CO 2 production rate was set constant with time, the δ 13 C Rs was adjusted to changing tracer content for simulations of the labelling experiment (see Sect. 2.3.2 below).Gravel below the soil was assumed to exhibit no respiratory CO 2 production.Porosity (ε a and ε w ), temperature and pH were set constant with time and soil depth.The balance equation (Eq. 1) was combined with Eqs. ( 2) and ( 7)-( 9), resulting in For numerical solution, this equation was discretised using time steps t and depth steps z.This allows one to derive the CO 2 concentration c a (z,t+ t) in each layer after a time step t from the concentrations before the time step t in that layer (c a (z,t)) and in the adjacent layers below (c a (z+ z,t)) and above (c a (z− z,t)).In the bottom layer (depth L), the diffusive exchange occurred only with the layer above.Diffusive exchange with the air pores in the gravel below the soil was neglected, since CO 2 concentration in the soil at depth L and in the gravel were identical in the steady-state.Treatment of the top layer depended on the simulated situation, see Sect.2.3 below.
For model validation, analytical solutions of the mass balance equation (Eq. 1) were generated assuming steady-state conditions (no concentration change with time) and homogenous distribution of respiration with soil depth.For diffusive regimes, the analytical solution was derived according to Cerling (1984).For diffusive-advective regimes, the analytical solution was similar to that of Camarda et al. (2007) and Kayler et al. (2010b), as both groups studied diffusive-advective regimes with a gas reservoir at the bottom of the soil instead of homogeneous production.For CO 2 mole fraction, numerical model results agreed within 0.2 % with analytically-derived CO 2 mole fraction at all depths.Numerically-derived δ 13 C was within 0.009 ‰ of analytically-derived δ 13 C. Furthermore, model estimates perfectly agreed with results presented by Cerling (1984) for the soil parameters given in that study.

Field labelling experiment
The 13 CO 2 / 12 CO 2 field labelling experiment, described in detail by Gamnitzer et al. (2009), was conducted at Grünschwaige Grassland Research Station (Schnyder et al., 2006).The soil at the experimental site was mineral soil (inceptisols), which was used as arable land for more than 40 years before conversion to grassland in 1999 (Schnyder et al., 2006).The temperate grassland ecosystem was continuously labelled for 2 weeks, and ecosystem respiration was measured every night.For this purpose, a chamber system was used, where the chambers were open at their top to the atmosphere ("open-top chambers"), and flushed with air.The label was applied during daytime hours by altering the δ 13 C of CO 2 in the chamber headspace air, while CO 2 mole fraction was kept similar to ambient.The δ 13 C of the CO 2 inside the chamber, to which the plants were exposed during photosynthesis, was −46.9 ‰.
Each night during the labelling experiment, ecosystem respiration was measured in the field using two different approaches: first, closed chamber measurements were conducted from sunset until approximately midnight; subsequently, open chamber measurements followed for the rest of the night (Fig. 1).For a description of the two respiration measurement approaches in the field see below.The CO 2 mole fraction and δ 13 C were analysed in the field with an infrared gas analyser (LI 7000; Li-Cor, Lincoln, NE, USA) and a continuous-flow isotope-ratio mass spectrome-ter (Delta Plus Advantage; Thermo Electron, Bremen, Germany) interfaced with a Gasbench II (providing sample gas separation via a built-in gas chromatograph, and sample and reference gas injection to the mass spectrometer; Thermo Electron, Bremen, Germany) (Schnyder et al., 2004).To ensure synchronous analysis of both quantities for the Keeling plots (see Sect. 2.2.2 below), CO 2 mole fraction was substituted by CO 2 peak area for the Keeling plots.Schnyder et al. (2004) demonstrated a proportional relationship between CO 2 mole fraction and CO 2 peak area.Measurement uncertainty of the mass spectrometer (SD of replicate measurements) was 0.09 ‰ for δ 13 C, and corresponded to ∼2 µmol mol −1 for the CO 2 peak area.

Open chamber approach to measure ecosystem respiration
For the open chamber (more exactly termed steady-state flow-through system, Livingston and Hutchinson, 1995) respiration measurements, the open-top chambers were flushed with air, and CO 2 mole fraction and δ 13 C were analysed in air entering and leaving the chamber.Differences between inlet and outlet were attributed to respiratory CO 2 production of the ecosystem enclosed in the chamber according to mass balance equations.The total CO 2 flux from the ecosystem into the chamber headspace, F efflux , was calculated as and the δ 13 C of ecosystem CO 2 efflux, δ 13 C efflux , as F air is the air flow through the chamber (corresponding to 100 L min −1 at standard conditions), A chamber the chamber base area (0.83 m 2 ).C in and C out are the CO 2 mole fractions (µmol mol −1 ) at the chamber inlet and outlet, and δ 13 C in and δ 13 C out are the respective δ 13 C values.

Closed chamber approach to measure ecosystem respiration
For the closed chamber (more exactly termed non-steadystate non-flow-through system, Livingston and Hutchinson, 1995) respiration measurements, the chamber air supply was disconnected.The chamber was lifted and then placed back in its original position immediately before the beginning of closed chamber measurements.The lifting flushed the labelled air from the chamber headspace and replaced it with ambient air.Thus, the mole fraction and δ 13 C of chamber headspace CO 2 at chamber closure in the labelled plots were the same as those in the unlabelled control measurements.The chamber top was then closed with a lid.Subsequently, the CO 2 mole fraction and δ 13 C were monitored by analyzing 6 consecutive samples (1 sample every 120 s) within a measurement cycle.Sample air was pumped continuously from the chamber headspace to the analysers at ∼1.5 L min −1 at standard conditions (corresponding to a turnover time of 7.3 h for the chamber headspace air).The air removed for sampling was replaced by ambient air entering the chamber through an opening of 1-2 cm diameter.
Assuming advective flow through this opening, the replacement air had the same mole fraction and δ 13 C of CO 2 as the chamber headspace air at chamber closure.It accounted for ∼3 % of the total headspace volume of the chamber by the end of a measurement cycle.Thus, replacement air slightly diluted the efflux signal in the chamber headspace.
From the time course of the CO 2 increase, F efflux was calculated as where C is the observed increase in CO 2 mole fraction in the chamber headspace during a time interval t, and V chamber the chamber volume (660 L, corrected for dilution with ambient air during the measurement cycle).The δ 13 C efflux was determined with the Keeling plot approach (Keeling, 1958;see Pataki et al., 2003 for applicationn to terrestrial ecosystem research).The 6 samples analysed in the measurement cycle following chamber closure were pooled in one Keeling plot, resulting in an intercept reflecting ecosystem δ 13 C efflux .The Keeling plot intercepts are invariant to the dilution of the efflux signal with background air.

Simulation runs
Model input parameters characterizing conditions for CO 2 transport in the soil were determined for the Grünschwaige field site (Table 1).The soil of depth L = 25 cm was divided into n = 125 layers of thickness z = 2 mm.This high depth resolution along with short time steps t, ranging between 1 s and 12 s, ensured sufficient accuracy of the discrete mass balance approximation and model stability.During daytime labelling, a chamber pressurization of 5 Pa above ambient was observed due to high daytime air flow (Gamnitzer et al., 2009).This pressurization might have caused vertical (downwards) advection of soil air during daytime labelling.The impacts of this potential chamber artifact and of the dissolution of labelling CO 2 in soil water on the disequilibrium effect were investigated independently.For this purpose, model runs were performed including or excluding the individual mechanisms.

Step changes in δ 13 C of atmospheric CO 2
This simulation investigated the disequilibrium effect that would result from changes in δ 13 C of chamber headspace CO 2 .In the labelling experiment, such changes occurred at the beginning of the closed chamber measurements, when the labelled air in the chamber headspace was substituted with ambient air.Thus, step changes of δ 13 C of CO 2 in the atmospheric layer (δ 13 C atm ) from −8.5 ‰ (ambient conditions, see Fig. 1) to −46.9 ‰ (labelling conditions, see Fig. 1), and vice versa, were simulated.To exclude disequilibrium effects not related to changes in δ 13 C atm , all other parameters (including δ 13 C Rs ) were kept constant and advection was excluded.Soil CO 2 efflux was derived from the simulated CO 2 concentration according to Fick's First Law: where c a is the concentration difference at the soil surface (between the air pores of the uppermost soil layer and the overlying atmosphere).The δ 13 C efflux was derived from the ratio of the simulated 12 CO 2 and 13 CO 2 effluxes.

Labelling experiment and chamber-based respiration measurements
To simulate CO 2 mole fraction and δ 13 C during the labelling experiment, boundary conditions for the atmospheric layer were chosen according to the respective chamber mode (Fig. 1).First, the model was run under ambient conditions, keeping CO 2 mole fraction and δ 13 C in the atmospheric layer at fixed values (371 µmol mol −1 and −8.5 ‰, see Fig. 1), until soil profiles of CO 2 and δ 13 C reached steady-state.
Then closed chamber measurements of δ 13 C efflux of the unlabelled ecosystem (control) were simulated.For closed chamber simulations, soil CO 2 efflux and shoot-respired CO 2 were mixed with ambient (background) air in the chamber headspace.Analogous to Keeling plot sampling during the field measurements, 6 consecutive values of simulated atmospheric layer CO 2 mole fraction and δ 13 C in 2 min intervals were pooled to generate a Keeling plot.Subsequently, conditions during open chamber measurements were simulated by forcing CO 2 mole fraction and δ 13 C in the atmospheric layer to be constant for 7 h (fraction of the dark period not covered by closed chamber simulations).Then, a daytime labelling period of 16 h followed: the CO 2 in the atmospheric layer was kept constant at labelling conditions (367 µmol mol −1 and −46.9 ‰, see Fig. 1), and δ 13 C Rs was adjusted to include a fractional contribution of labelled carbon according to the results of Gamnitzer et al. (2009) (see below for details).The cycle of modelling nighttime measurements in closed and open chambers and daytime labelling was repeated to simulate the 2-week-long continuous labelling experiment.
To account for the increasing amount of label in the respiratory source during the experiment, δ 13 C Rs was adjusted from day to day according to the "true" time course of tracer.The latter was derived from the fit (Gamnitzer et al., 2009, see also Fig. 2, solid line) to the open chamber data (Fig. 2, open circles).To partition this signal into belowground (soil) and aboveground (shoot) respiratory CO 2 production (which are required as model input parameters), three respiratory sources were distinguished.The first, decomposition of soil organic matter, was located in the soil, did not respire any tracer (δ 13 C constant at −26.7 ‰) and contributed 52 % of ecosystem respiration (Gamnitzer et al., 2009).The other two sources reflected aboveground and belowground autotrophic respiration, where each was assumed to contribute 50 % of autotrophic respiration.Both supplied recentlyassimilated carbon from a labelled pool (δ 13 C changed from −26.7 ‰ to −64.4 ‰ with a pool half-life of 2.6 d; Gamnitzer et al., 2009).In total, δ 13 C Rs changed from −26.7 ‰ to −37.8 ‰ for the belowground source and from −26.7 ‰ to −63.5 ‰ for the aboveground source in the simulation of the 14-days-long labelling period.In contrast, soil and shoot respiration rates were kept constant during a simulation run.

Sensitivity analysis and model assumptions
To investigate model sensitivity, simulation runs were performed with individual input parameters varying within the ranges given in Table 1.These ranges represent the uncertainty in determination of the input parameters.The partitioning of the autotrophic respiratory source to belowground and aboveground fractions (assumed 50 %:50 %, see above) was allowed to vary between 20 %:80 % and 80 %:20 %.Diffusivity of CO 2 in the soil was derived from various models to account for the uncertainty connected with the choice of a D soil model.
Several assumptions behind the model were chosen according to the specific conditions at this particular field site.
The assumption of homogeneous distribution of pore size with depth is based on the past land use of the site as arable land, including periodic tillage.With conversion to grassland 8 years before the labelling experiment, differentiation of pore size distribution could have started.To account for this, the uncertainty range includes the observed variation in porosity between the soil surface (0-3 cm average) and a depth of 7-10 cm (Table 1).Similarly, depth variation in pH is neglected, in particular because the site shows calcareous characteristics with high buffering capacity.Variations of soil pH in the rhizosphere can be high, but are limited spatially (few millimeters around the growing parts of roots, see e.g.Revsbech et al., 1999) and temporally (within days, see e.g.Flessa and Fischer, 1992).Therefore, they were not considered in the present study.
Disregarding respiratory CO 2 production in the gravel below the soil implied that the entire production of the observed CO 2 efflux was partitioned to the soil layer.Since this corresponded to a shift in the depth distribution of the respiratory source, sensitivity of the model results to variations in the depth distribution were investigated.Furthermore, a one-dimensional model was used in the present chamber investigation.For the upper half of the soil layer, this simplification was appropriate due to mechanical suppression of lateral exchange by the chamber walls.The chambers were inserted into the soil via a soil collar to a depth of 12 cm, compared to a soil depth of 25 cm.Below the soil collar depth, lateral exchange processes were neglected according to the requirements provided by Nickerson and Risk (2009b,c) on soil diffusivity, air-filled porosity and chamber deployment time.Also the chamber used here was about 10 times larger in diameter than the one studied by Nickerson and Risk, minimizing edge effects.Furthermore, the influence of the atmospheric tracer on δ 13 C in soil pores via gas exchange decreases with soil depth, suggesting that lateral effects were small below soil collar depth.

Experimental tracer time series of nocturnal ecosystem CO 2 efflux
The The SD of the Keeling plot intercepts (parameter of linear fit) was 0.86 ‰ on average for an individual Keeling plot, with R 2 = 0.989 and CO 2 mole fraction covering a range of 120 µmol mol −1 .Potential biases due to choice of regression method (ordinary least squares regression vs. geomet-ric mean regression) and mixing model approach (Keeling vs. Miller-Tans) were recently discussed (Pataki et al., 2003;Zobitz et al., 2006;Kayler et al., 2010a).Here, the average deviations were 0.09 ‰ between regression methods and 0.07 ‰ between mixing models approaches.In contrast, the SD between Keeling plots in replicate ecosystem plots was 4.4 ‰.

Simulation of CO 2 in soil air in ambient conditions
Modelled CO 2 mole fraction increased with depth from 371 µmol mol −1 in the overlying atmosphere to 6500-18600 µmol mol −1 at the bottom of the soil (Fig. 3a,c).The δ 13 C of CO 2 changed continuously from −8.5 ‰ in the atmospheric layer to values between −21.6 ‰ and −22.1 ‰ at the bottom of the soil (Fig. 3b,d).The δ 13 C profile corresponded to the theoretical mixing line (analogous to that illustrated by Bowling et al. (2009) for CO 2 in a snowpack) between atmospheric air (−8.5 ‰) and soil air (−22.3‰), with the latter 4.4 ‰ enriched (Cerling et al., 1991) relative to δ 13 C Rs (−26.7 ‰).The gradients of both profiles were large in the top few centimeters of the soil and decreased with depth.Accordingly, the main changes occurred above the soil collar depth of 12 cm.
Sensitivity of modelled profiles to uncertainties in input parameters was smallest for temperature, with changes of soil air CO 2 mole fraction within 170 µmol mol −1 and changes in δ 13 C within 0.1 ‰.Sensitivity was largest for the depth distribution of CO 2 production in the soil: up to a doubling of CO 2 mole fraction was predicted if production occurred deeper in the soil.In contrast, δ 13 C varied little (within 0.3 ‰).All selected input parameter values provided realistic depth profiles of CO 2 mole fraction (e.g., Amundson and Davidson, 1990) and δ 13 C (e.g., Cerling, 1984;Amundson et al., 1998).The amount of CO 2 in the dissolved phase was 9.5 to 34 times that in soil air.Conversely, CO 2 mole fraction and δ 13 C in soil air were independent of dissolution (data not shown).

Simulation of step changes in δ 13 C atm
First, a step change of δ 13 C atm from −8.5 ‰ (ambient conditions) to −46.9 ‰ (labelling conditions) was studied, with δ 13 C Rs kept constant at −26.7 ‰ (Fig. 4a).Immediately following the change of δ 13 C atm , the modelled δ 13 C efflux became 26.2 ‰ enriched relative to δ 13 C Rs (Fig. 4c).Thereafter, δ 13 C efflux decreased asymptotically towards δ 13 C Rs .Eventually (within hours to days; see below), the soilatmosphere system reached a new isotopic steady-state.Then, a step change in δ 13 C atm in the opposite direction caused corresponding changes in the other isotopic direction (Fig. 4b), with an initial shift in δ 13 C efflux to 26.2 ‰ more depleted values.Again, the system tended to a new steady-state (Fig. 4d).  1) is indicated by the thin dashed or dotted lines.Upper panels (a, b): depth profiles when depth distribution of CO 2 production in soil (dashed) and soil respiration rate (dotted), respectively, were varied.Lower panels (c, d): depth profiles when soil porosity (dashed) and temperature (dotted), respectively, were varied.

Biogeosciences
These model results were derived from the independent consideration of 12 CO 2 and 13 CO 2 pools and fluxes (Fig. 4el; for clarity, the illustration is limited to the top soil layer).This included the following steps: (1) The change in δ 13 C atm from ambient to labelling (more 13 C-depleted) conditions corresponded to an increase of 0.16 µmol mol −1 of the atmospheric 12 CO 2 pool and a decrease of 0.16 µmol mol −1 of the atmospheric 13 CO 2 pool.(2) These changes of atmospheric CO 2 pool sizes caused changes in the differences between soil and atmospheric CO 2 pools, which led to a slightly decreased 12 CO 2 and a slightly increased 13 CO 2 diffusive soil efflux (Eq.16).Note that the changes in the CO 2 differences across the soil surface were small (0.16 µmol mol −1 ) compared to the CO 2 differences (535 µmol mol −1 for 12 CO 2 and 5.9 µmol mol −1 for 13 CO 2 ).Nevertheless, these small relative changes in the differences (and thus in the effluxes) of 12 CO 2 and 13 CO 2 resulted in a big shift (26.2 ‰) in δ 13 C efflux .(3) The altered fluxes, in turn, increased the soil pool of 12 CO 2 and decreased that of 13 CO 2 .(4) After some time, the system reached a new steady-state with the original fluxes, but with altered 12 CO 2 and 13 CO 2 pool sizes.(5) The switch back to δ 13 C atm of ambient air again changed the atmospheric CO 2 pool sizes, in this case 12 CO 2 was decreased and 13 CO 2 was increased by 0.16 µmol mol −1 .(6) Accordingly, this led to an increased 12 CO 2 and a decreased 13 CO 2 soil efflux, changing δ 13 C efflux to a more depleted value.Overall, steps (1) to (6) acted as a tracer flux caused by soil-atmosphere isotopic disequilibria: the δ 13 C of the labelled CO 2 was transferred from the atmosphere into the soil (although both the 12 CO 2 and the 13 CO 2 fluxes were directed from the soil to the atmosphere) and vice versa, respectively, via diffusion.It should be noted that during all simulated transitions the 12 CO 2 and 13 CO 2 pool sizes and fluxes changed, while total CO 2 -which is the sum of both isotopologues -remained constant.
Dissolution of CO 2 in soil water delayed the progression to the new steady-state following a change in δ 13 C atm (Fig. 5).The δ 13 C efflux reached δ 13 C Rs within 0.4 ‰ (corresponding to 1 % of the difference between ambient and labelled CO 2 ) after 15.4 h when dissolution was included in the simulation, and after 49 min (19 times faster) when dissolution was excluded.This relationship of simulated re-equilibration times corresponded to the ratio of total (gaseous + dissolved phase) CO 2 to gaseous CO 2 in the soil.In contrast, dissolution did   (c, d) δ 13 C efflux (solid line) and δ 13 C Rs (dotted line, constant).(e, f) 12 CO 2 and (g, h) 13 CO 2 mole fraction in the atmospheric and top soil layer, and the mole fraction difference between these two layers.Bottom (i-l): Schematic illustration of the mechanism underlying abiotic tracer diffusion, treating 12 CO 2 and 13 CO 2 as separate gases.Squares, atmospheric and soil CO 2 pools; arrows, CO 2 fluxes; dotted lines indicate pools and fluxes prior to the changes; numbered events in the bottom scheme (i-l) match with those in the upper panels (e-h).(i) Unlabelled system in steady-state.(j) Tracer application and associated transitions, namely (1) change in δ 13 C atm to more depleted value (corresponding to more 12 CO 2 and less 13 CO 2 ), (2) change in CO 2 diffusive fluxes due to changes in soil-atmosphere CO 2 gradient, and (3) change in soil CO 2 pool due to altered fluxes.(k) Labelled system in steady-state with (4) fluxes exhibiting the original δ 13 C. (l) Closed chamber measurement and associated transitions, namely (5) change in δ 13 C atm to ambient value, (6) change in CO 2 diffusive fluxes due to changes in soil-atmosphere CO 2 gradient, and (7) change in soil CO 2 pool due to altered fluxes.not affect the magnitude of the initial change in soil CO 2 efflux.This was driven by the step change in δ 13 C atm but was independent of the size of the soil CO 2 pool.

Simulated tracer time series of nocturnal ecosystem CO 2 efflux
Simulated δ 13 C efflux predicted by simulated Keeling plot intercepts (Fig. 6, dashed line) in the labelling experiment was depleted compared to δ 13 C Rs (Fig. 6, solid line, taken from Fig. 2).When simulations of the closed chamber measurements considered only the diffusion mechanism, then the predicted disequilibrium effect was 1.8 ‰ on average (Fig. 6a).When, in addition, downward advection of soil air during daytime tracer application was included, then the predicted disequilibrium effect increased to 3.6 ‰ (Fig. 6b).When dissolution of CO 2 in soil water was included in addition to diffusion, the predicted disequilibrium effect was 4.5 ‰ (Fig. 6c).When diffusion, advection and dissolution were all included in the simulation, the predicted disequilibrium effect was 9.5 ‰ (Fig. 6d).This largely agreed with the observed disequilibrium effect of 11.2 ‰ (Fig. 6, black squares; taken from Fig. 2).Sensitivity analysis (Fig. 7) shows that, within the uncertainties in model input parameters, simulations excluding dissolution did not reproduce the magnitude of the observed disequilibrium effect.
The magnitude of the disequilibrium effect resulting from Keeling plot non-linearity was derived from simulations where δ 13 C atm remained unchanged and advection was excluded.These conditions were met when Keeling plots were derived before the onset of labelling (see also Fig. 1).These Keeling plots yielded disequilibrium effects smaller than 0.05 ‰.This work demonstrated that isotopic disequilibria in the soil CO 2 pool can explain the divergence between nocturnal ecosystem δ 13 C efflux and ecosystem δ 13 C Rs which was observed in a grassland tracer experiment.This 13 CO 2 / 12 CO 2 flux disequilibrium appeared as a transient feature in closed chamber studies (in which the Keeling plot approach was used).A change of δ 13 C atm at the beginning of the closed chamber Keeling plot measurements was shown to potentially induce the proposed disequilibrium.Simulations with a soil CO 2 transport model accounting for diffusion, advection and dissolution reproduced most (9.5 ‰) of the observed disequilibrium effect (11.2 ‰).In contrast, simulations excluding either dissolution or advection or both accounted for less than half of the observed disequilibrium effect.This strongly suggests that, besides diffusion, both dissolution and advection contributed significantly to the observed disequilibrium effect and, hence, that soil CO 2 pools and species other than gaseous CO 2 (e.g., dissolved bicarbonate) were involved.The disequilibrium effect strongly affected data interpretation in terms of ecosystem respiration, since its magnitude (11.2 ‰) corresponded to ∼30 % of the tracer signal (difference in δ 13 C atm between ambient (−8.5 ‰) and labelling conditions (−46.9 ‰)) in our experimental study.If interpreted in terms of tracer content of soil respiration, the disequilibrium effect would have been even larger.A similar phenomenon (disequilibrium or "abiotic" tracer flux) was noted by Subke et al. (2009) who used a diffusion model and a much stronger label (δ atm ∼23 000 ‰ as compared to −46.9 ‰ in our study).The simulation of the tracer time series suggested that dissolution of CO 2 in soil water significantly influenced the magnitude of the disequilibrium effect observed in the present experimental study.Dissolved CO 2 represented a reservoir allowing storage of a large amount of label CO 2 in the soil in addition to CO 2 in soil air pores.Involvement of dissolved CO 2 in soil CO 2 transport processes delayed the equilibration between CO 2 in soil air and the overlying atmosphere and slowed re-equilibration of δ 13 C efflux .Dissolved CO 2 was modelled as part of soil CO 2 transport assuming instantaneous exchange between gaseous and dissolved  phase.This assumption was valid if the gaseous-dissolved phase chemical equilibration was fast compared to the isotopic equilibration between soil air CO 2 and overlying atmosphere.The latter occured within hours to days.Presumably, gaseous-dissolved phase equilibration was much faster, as it was probably catalysed by carbonic anhydrase.Carbonic anhydrase was previously found in soil inhabitating organisms such as bacteria (Kusian et al., 2002;Mitsuhashi et al., 2004) and fungi (Aguilera et al., 2005;Amoroso et al., 2005;Klengel et al., 2005;Mogensen et al., 2006), as well as in nonphotosynthetic plant organs and tissues (Raven and Newman, 1994), particularly roots (Viktor and Cramer, 2005) and growing root tips (Chang and Roberts, 1992).Furthermore, Seibt et al. (2006) and Wingate et al. (2008) provided evidence for the presence of carbonic anhydrase in the upper soil horizons, accelerating the hydration of bicarbonate by a factor of 80-1000 (which corresponded to equilibration within less than 1 s).Considering these timescales, participation of a major fraction of dissolved CO 2 in soil gas transport is likely, even if isotopic equilibrium was not fully reached.However, Reardon et al. (1979) found that δ 13 C of CO 2 species in groundwater was consistent with complete isotopic equilibration of CO 2 in soil water with CO 2 in soil gas.In agreement with the suggestion of Högberg et al. (2008), the present findings strongly suggest (at least partial) isotopic equilibration of label CO 2 with CO 2 species dissolved in soil water.
The capacity of the soil to store isotopically labelled CO 2 is expected to be largest under alkaline conditions, as the amount of CO 2 in the dissolved phase increases with pH.This is consistent with the re-equilibration of δ 13 C efflux following a change in δ 13 C atm , since the simulated reequilibration time increases strongly with pH (Fig. 8).At low pH values (below ∼6), the concentration of dissolved carbon species is dominated by H 2 CO 3 (aq).The H 2 CO 3 (aq) concentration is constant for a given temperature and CO 2 concentration in the air, and approximately the same amount of carbon is dissolved as H 2 CO 3 (aq) and in the gaseous phase as CO 2 , if volumes of water and air are equal (Bunsen coefficient, which is the ratio c w /c a , ∼1).At pH values above ∼6, HCO − 3 dominates the dissolved carbon species.As the HCO − 3 concentration increases exponentially with pH, the CO 2 storage capacity of soil water increases strongly with alkalinity.Under alkaline conditions a multiple of the amount of carbon in the gaseous phase (CO 2 ) is dissolved in an equal volume of water (Bunsen coefficient 1).In the present study (pH = 7.5) the Bunsen coefficient was 12.4.In contrast, at the experimental site of Subke et al. (2009) the pH was low (4.5), indicating that dissolved CO 2 played a much smaller role in that study than in our example.Downward advection of soil air also affected our δ 13 C efflux measurements.Chamber headspace pressurization during daytime tracer application (Gamnitzer et al., 2009) presumably displaced soil air masses downwards (Lund et al., 1999), as the soil collars of the chambers restricted lateral movement.The δ 13 C efflux measurements were conducted during nighttime and thus subsequent to the daytime phase of advective transport.Nevertheless, the simulations suggest that the measurements were influenced by the preceding pressurization.
Mechanisms which were not included in the simulation may have accounted for the residual disequilibrium effect of 1.7 ‰ between modelled and observed δ 13 C efflux .These mechanisms included temporal changes of parameters (such as temperature, soil water content and respiration rate) during the course of the labelling experiment, diffusion in the dissolved phase, advection of soil water or incomplete isotopic equilibration between gaseous and dissolved CO 2 .

Relevance to other experimental conditions
Isotopic labelling signals of similar magnitude are frequently applied in Free-Air CO 2 Enrichment (FACE) experiments, which are usually operated at δ 13 C of elevated CO 2 between −15 ‰ and −20 ‰ (e.g., Nitschelm et al., 1997;Matamala et al., 2003;Asshoff et al., 2006;Keel et al., 2006;Pregitzer et al., 2006;Taneva et al., 2006).When FACE experiments are combined with measurements of δ 13 C efflux (Torn et al., 2003;Søe et al., 2004;Pregitzer et al., 2006;Taneva et al., 2006;Taneva and Gonzalez-Meler, 2011) and fumigation with isotopically different CO 2 is restricted to daytime (e.g., Lewin et al., 1994;Zanetti et al., 1996;Miglietta et al., 1997;Hendrey et al., 1999;Dickson et al., 2000;Edwards et al., 2001;Miglietta et al., 2001;Reich et al., 2001;Pepin and Körner, 2002;Talhelm et al., 2007), the measurements are potentially affected by disequilibrium effects as observed in the present study, if these measurements are performed shortly after the nighttime switch-off of the fumigation.Disequilibrium effects on δ 13 C efflux are also expected in pulsechase experiments, where highly enriched 13 CO 2 is applied (Subke et al., 2009, see Fig. 9 for estimates at our study site).However, the time course of disequilibrium effects must be considered, since the disequilibrium is largest immediately after its initiation (the atmospheric change) and decreases with time (see Fig. 4).Thus, early initiation of sampling and short sampling duration will increase disequilibrium effects comprised in a chamber measurement.In our grassland experiment, the disequilibrium effect was relevant for hours to days.This was consistent with observations in a boreal forest ecosystem, where the disequilibrium ("abiotic") tracer flux was significant for 48 h (Subke et al., 2009).
In some instances chamber techniques have involved a lowering of the chamber headspace CO 2 concentration at the onset of the measurements (Flanagan et al., 1996;Buchmann and Ehleringer, 1998;Ohlsson et al., 2005).This procedure alters not only the soil-atmosphere CO 2 gradient but also the 12 CO 2 and 13 CO 2 gradients, and thus δ 13 C efflux , as shown by Ohlsson et al. (2005).In a theoretical investigation considering CO 2 in soil air, Nickerson and Risk (2009c) predicted a disequilibrium effect (deviation between δ 13 C Rs and δ 13 C efflux observed with such chambers) of up to 15 ‰.This disequilibrium effect would be even larger when dissolution of CO 2 in soil water occurred.This applies when the gaseous-dissolved phase chemical equilibration is fast compared to the isotopic equilibration between soil air CO 2 and overlying atmosphere (such as in the presence of carbonic anhydrase in the soil).Natural variability in atmospheric CO 2 would cause the same disequilibrium effect as a change of headspace CO 2 inside the chambers.Diurnal cy- cles of δ 13 C atm can show amplitudes of ∼10 ‰ (e.g., Schnyder et al., 2004).Using a diffusion-based model Nickerson and Risk (2009a) predicted a disequilibrium effect within 0.05 ‰ resulting from daytime-nighttime changes of both atmospheric CO 2 concentration and δ 13 C.However, inclusion of the dissolution mechanism would likely multiply this disequilibrium effect.

Fig. 2 .
Fig. 2. δ 13 C of nocturnal ecosystem CO 2 efflux observed by the open (open circles; Gamnitzer et al., 2009) and closed (black squares) chamber methods during 14 d of continuous labelling.Error bars: SE of replicate plots, n=2−10.The line represents the fit to the open chamber data(Gamnitzer et al., 2009).

Fig. 3 .
Fig.3.Modelled depth profiles (thick black lines) of soil CO 2 mole fraction C (a, c) and isotopic composition δ 13 C (b, d) under ambient conditions (the beginning of the labelling experiment) for soil conditions observed at the experimental field site.Sensitivity of each to variations in input parameters within the observed range (Table1) is indicated by the thin dashed or dotted lines.Upper panels (a, b): depth profiles when depth distribution of CO 2 production in soil (dashed) and soil respiration rate (dotted), respectively, were varied.Lower panels (c, d): depth profiles when soil porosity (dashed) and temperature (dotted), respectively, were varied.

Fig. 4 .
Fig. 4. Conceptual model of the influence of a step change in δ 13 C atm on δ 13 C efflux .The δ 13 C atm was switched from ambient (−8.5 ‰) to labelling conditions (−46.9 ‰) (left panels), and vice versa (right panels).(a, b) δ 13 C atm (solid line) and δ 13 C Rs (dotted line, constant).(c,d) δ 13 C efflux (solid line) and δ 13 C Rs(dotted line, constant).(e, f)12 CO 2 and (g, h)13 CO 2 mole fraction in the atmospheric and top soil layer, and the mole fraction difference between these two layers.Bottom (i-l): Schematic illustration of the mechanism underlying abiotic tracer diffusion, treating 12 CO 2 and 13 CO 2 as separate gases.Squares, atmospheric and soil CO 2 pools; arrows, CO 2 fluxes; dotted lines indicate pools and fluxes prior to the changes; numbered events in the bottom scheme (i-l) match with those in the upper panels (e-h).(i) Unlabelled system in steady-state.(j) Tracer application and associated transitions, namely (1) change in δ 13 C atm to more depleted value (corresponding to more 12 CO 2 and less 13 CO 2 ), (2) change in CO 2 diffusive fluxes due to changes in soil-atmosphere CO 2 gradient, and (3) change in soil CO 2 pool due to altered fluxes.(k) Labelled system in steady-state with (4) fluxes exhibiting the original δ 13 C. (l) Closed chamber measurement and associated transitions, namely (5) change in δ 13 C atm to ambient value, (6) change in CO 2 diffusive fluxes due to changes in soil-atmosphere CO 2 gradient, and (7) change in soil CO 2 pool due to altered fluxes.

Fig. 5 .
Fig.5.Modelled δ 13 C efflux following a step change (at time 0) in δ 13 C atm from ambient (−8.5 ‰) to labelling conditions (−46.9 ‰) when dissolution of CO 2 in soil water was included (solid line, see also Fig.4c) or excluded in the CO 2 transport model (dotted line).δ 13 C Rs was kept constant at −26.7 ‰ (dashed line).When lines are overlapping, only the dotted line is shown.

Fig. 6 .
Fig. 6.The δ 13 C Rs estimated from open chamber measurements (solid lines), and δ 13 C efflux derived from measured (dots; error bars: SE of replicate plots, n = 2−10) and modelled (dashed lines) Keeling plot intercepts in closed chambers.Simulations exclude (a, b) or include (c, d) dissolution of CO 2 in soil water, and exclude (a, c) or include (b, d) advection during daytime tracer application.The grey shaded areas indicate the sensitivity of modelled Keeling plot intercepts to variations of input parameters (seeTable 1 for range).

Fig. 8 .
Fig. 8.Modelled re-equilibration time, the time interval between a step change in δ 13 C atm from labelling (−46.9 ‰) to ambient (−8.5 ‰) conditions and δ 13 C efflux reaching δ 13 C Rs within 0.4 ‰ (corresponding to 1 % of the difference between ambient and labelled CO 2 ).Simulations included dissolution for various pH values (closed squares) or excluded dissolution (dashed line).

Fig. 9 .
Fig.9.Modelled δ 13 C efflux following pulse labelling with highly enriched CO 2 (20 atom% 13 CO 2 ) for 1 h.Dissolution of CO 2 in soil water was included (solid line) or excluded (dotted line) in the CO 2 transport model.δ 13 C Rs was kept constant at −26.7 ‰ (dashed line).

Table 1 .
Parameters characterizing conditions for CO 2 transport in the soil at the Grünschwaige field site.
Schematic sequence of labelling experiment, including chamber headspace conditions (cl.: closed) of air flow, CO 2 mole fraction and δ 13 C of CO 2 .The latter are shown as averages observed during the labelling experiment, and were used as input parameters in the model simulation.For closed chamber headspace, values are given at chamber closure.