We investigated spatial and temporal variability in the carbon stable isotope ratio (δ13C) of soil heterotrophic respiration in a deciduous needle-leaf forest in Japan for 3 years. We used high-precision isotope measurement coupled with a sampling system optimized for soil respiration to capture this variability under natural conditions. The limitations of chamber-based measurements combined with spatial variation created a representation error that prevented precise estimates of flux-weighted mean δ13C, but we could nonetheless characterize the δ13C variations intrinsic to heterotrophic respiration. In the absence of root respiration, δ13C exhibited significant seasonal variation, with a greater range than in previous models. In a root-exclusion plot, δ13C was lowest at high temperatures but showed a different seasonal course from that of CO2 efflux. A simple model explained the seasonal variation in δ13C using interpool differences in δ13C of decomposed organic matter, in the temperature dependence of decomposition rates, and in the seasonal changes in pool size. The characteristic seasonality of δ13C appears to be associated with the properties of the forest, including litterfall patterns.
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 The carbon stable isotope ratio (commonly expressed in simplified form, δ13C, whose definition is described in section 2.4 of this paper) of atmospheric CO2 provides important information about the global carbon budget [e.g., Tans et al., 1993]. Combined with consecutive measurements of the atmospheric CO2 mixing ratio ([CO2]), time series of the δ13C values of atmospheric CO2 have been used to estimate the relative roles of the oceans and terrestrial biosphere as net CO2 sinks [Heimann and Keeling, 1989; Ciais et al., 1995a, 1995b; Francey et al., 1995; Keeling, 1995; Fung et al., 1997; Bousquet, 1999a, 1999b; Rayner et al., 1999]. This method is based on the mass balance of CO2 and 13CO2 in the atmosphere. Atmospheric [CO2] and the δ13C of CO2 both fluctuate within the terrestrial biosphere in response to photosynthetic and respiratory fluxes. If the exchange of CO2 and 13CO2 between the atmosphere and the terrestrial biosphere operates under steady-state conditions, the flux-weighted mean δ13C of the CO2 assimilated by photosynthesis equals the flux-weighted mean δ13C of the CO2 released by respiration on an annual mean basis. However, the δ13C of atmospheric CO2 has been changed due to the release of 13C-depleted CO2 by combustion of fossil fuels. Hence, the time difference between photosynthetic uptake and respiratory release of CO2 by the terrestrial biosphere causes “isotopic disequilibrium” [e.g., Fung et al., 1997]. Estimates of carbon budgets using the δ13C of atmospheric CO2 depend strongly on the choice of values for this disequilibrium [Ciais et al., 1999]. When we use atmospheric tracer transport models instead of a single-box model of the atmosphere, the spatial and temporal distribution of the isotope disequilibrium must also be estimated.
 Evaluating the isotope disequilibrium in the atmosphere–biosphere CO2 exchange requires an accurate understanding of the isotopic signature of the respiratory CO2 flux from the terrestrial ecosystem into the atmosphere (Fba of equation (1a) in Fung et al. ). If we define the counter-flux of Fba (Fap) in this equation as net carbon assimilation, then Fba equals ecosystem respiration. This ecosystem respiration is subdivided into two components: autotrophic respiration by plants and heterotrophic respiration resulting from microbial decomposition of dead organic matter. The autotrophic respiration is directly linked to new carbon assimilated by means of photosynthesis, hence the isotopic signature from autotrophic respiration would immediately reflect the change in photosynthetic isotope discrimination. Assuming that an isotopic equilibrium exists between autotrophic respiration and carbon fixed by photosynthesis, Fap can be identified to net primary productivity (NPP) and Fba can be identified to heterotrophic respiration [Ciais et al., 2005]. To investigate the seasonal and interannual variability of the isotope disequilibrium related to atmosphere–biosphere CO2 exchange and its spatial distribution, it is important to accurately assess the δ13C of heterotrophic respiration. It must be noted that the modeled values of isotopic disequilibrium between newly formed phytomass and soil-respired CO2 are typically smaller than 1‰ (e.g., 0.33 to 0.56‰ [Heimann and Keeling, 1989; Ciais et al., 1995a, 1999; Fung et al., 1997; Scholze et al., 2003]).
 Recent studies have revealed that δ13C of ecosystem respiration (δ13CR) or soil respiration (δ13CR-soil) has significant spatial and temporal variability. Ekblad and Högberg  and Ekblad et al.  found that δ13C of soil respiration in a boreal mixed coniferous forest had seasonal variation in magnitude of nearly 5‰, and suggested potential linkage between the δ13C and above ground weather conditions 1–4 days before. Bowling et al.  reported that δ13C of ecosystem respiration observed at six coniferous forests showed strong linkage with the vapor saturation deficit of air 5–10 days earlier. The results of investigation made by McDowell et al.  showed that the δ13C of soil respiration had a variability associated with meteorological factors although the δ13C of ecosystem respiration was not controlled solely by either aboveground and belowground processes. In those studies, the variation in δ13C of soil respiration and/or ecosystem respiration was interpreted to reflect the fluctuation in photosynthetic isotope discrimination via autotrophic respiration within timescale of several days. In ecological aspects, the change of the δ13C of autotrophic respiration in rapid response to environmental factors has provided useful information about carbon cycle in terrestrial ecosystem. But we considered that correct understanding of natural variations in the δ13C of heterotrophic respiration would be desirable in the studies of large-scale atmosphere-terrestrial biosphere CO2 exchange using 13C information. Despite its importance, there is lacking in reliable measurement of the δ13C of heterotrophic respiration under natural conditions. Although Fung et al.  estimated the seasonal range of variation in the isotopic signature of Fba to be less than 0.3‰ everywhere in the world using their model, this conclusion has not been verified by field observations.
 Against this background, we set out to observationally validate model predictions of the seasonality of the δ13C of heterotrophic respiration [Fung et al., 1997] and of the isotopic disequilibrium [Fung et al., 1997; Scholze et al., 2003]. To support this goal, we must correctly measure the natural variability in δ13CR-soil. In this study, we conducted the following field observations:
 1. To assess the representativeness of the δ13CR-soil values measured by our chamber-based sampling method for a given spatial scale, we examined short-term temporal variations and spatial variations of δ13CR-soil with and without the influence of root respiration.
 2. To validate the model prediction that the δ13C of heterotrophic respiration has insignificant seasonality, we conducted regular fixed-point sampling in a deciduous Japanese needle-leaf forest for nearly 3 years.
2. Materials and Methods
2.1. Site Description
 We performed our measurements at the Tomakomai Flux Research site (42°44′N, 141°31′E) on Hokkaido Island, northern Japan, about 15 km inshore from the Pacific Ocean. The site is located in Tomakomai National Forest. The predominant tree species at the site was 45-year-old Japanese larch (Larix kaempferi Sarg.), interspersed with Japanese spruce (Picea jezoensis Sieb. et Zucc.) and mixed broadleaved species (Betula ermanii Cham., Ulmus davidiana var. japonica, Prunus jamasakura Sied. ex Koidz. etc.). The larch forest dominated 98 ha of the total 117 ha of the forest. In 1999, the overstory density was ca. 1087 stems ha−1, the total basal area was ca. 23.5 m2 ha−1, and the aboveground volume averaged 145 m3 ha−1. The tree canopy ranged from 12.4 to 17.2 m in height (14.6 m average), with a stem diameter at breast height (DBH) ranging from 15.8 to 25.0 cm (19.9 cm average). The forest canopy had a mean depth of 8.9 m and a leaf area index (LAI, m2; projected tree leaf area per m2 of ground area) of 2.0; its seasonality has been described by Hirata et al. . The forest understory was predominantly buckler fern (Dryopteris crassirhizoma Nakai), with occasional bracken fern (Dryopteris expansa Fr.-Jenkins et Jermy) and Japanese spurge (Pachysandra terminalis Sieb. et Zucc.). The average biomass of the understory was 1.24 t ha−1. Mean δ13C values of the plant leaves were −29.7‰ PDB (“PDB” denotes that the isotope ratio is expressed on a PeeDee Belemnite (PDB) basis) for Japanese larch, −31.5‰ PDB for the mixed broadleaved species, and −28.2‰ PDB for buckler fern, respectively (T. Nakadai, ex NIES, Japan, personal communication; sampling was conducted in 2000–2001; large part of the overstory leaves were collected from lower and shaded part of the forest canopy).
 The soil at the site, a well-drained arenaceous soil developed from volcaniclastic sediment, was homogeneous and was classified as an immature Volcanogenous Regosol (Pumice). The nutrient-poor soil was weakly acidic (pH 5.0 to 6.0), with high porosity. The litter layer was 1 to 2 cm thick. Below the litter layer is a mat of organic layer between 5 and 10 cm thick and containing abundant fine roots; the next-deepest layer is fragments of porous pumice stone (0.5–3.0 cm in diameter) with some coarse roots. Scarcely any roots are found below a depth of 20 cm. Bulk organic matter collected from the soil surface at 25 plots in the forest revealed δ13C values ranging from −27 to −29‰ PDB. There was a tendency common to all sampling plots that δ13C of the organic matter increased as decomposition progressed from fresh plant material to litter and from litter to soil organic matter (T. Nakadai, ex NIES, Japan, personal communication; sampling was conducted in 2000–2001).
 The site was essentially flat, with a slope of 1–2°. The altitude ranged from 115 to 140 m above sea level. The site was characterized by a humid continental climate with cold winters and cool summers. The monthly mean air temperature and total monthly precipitation observed at the nearest weather station (Tomakomai weather station, 42°37.3′N, 141°32.8′E, located ca. 14 km south of the study site) are shown in Figure 1. The 30-year (1971–2000) mean annual precipitation was approximately 1229 mm; mean annual temperature was 7.5°C, with the mean monthly temperature ranging from 20.3°C in August to −4.1°C in January. Although precipitation is generally heavier in summer, all weather parameters exhibited significant year-to-year variation during the 3 years of our observation (2002, 2003, and 2004).
 In this vegetation type at our study site, there was distinct seasonality in litterfall. Litterfall observed at 25 locations from 14 July (195 DOY) to 18 December (352 DOY) 2003 is shown in Figure 2. Litterfall was concentrated from October to November, and LAI decreased rapidly during this period [Hirata et al., 2007]. This distinct seasonality in the input of fresh leaf litter to the soil system would lead to seasonal changes in the composition of the respiration substrates and, as a result, may influence the δ13C of heterotrophic respiration.
 Our observations began in July 2002 and ended at the beginning of September 2004 because of extensive damage caused to the forest by typhoon 200418. In the typhoon event, more than 90% of trees were broken in the trunk part or pulled out by the root. The forest canopy had lost and the soil was disturbed seriously. The ecosystem in the site no longer has characteristics as a forest. Hence we abandoned further research at the site.
2.2. Sampling of Soil-Respired CO2
 The main issues in the determination of the δ13C of heterotrophic respiration are how to eliminate the influence of autotrophic (root) respiration from total soil CO2 efflux and how to determine the δ13C of soil CO2 efflux without introducing measurement artifacts [e.g., Högberg et al., 2005; Ohlsson et al., 2005].
 In terms of the separation of heterotrophic respiration, the usability and limitations of the major approaches have been reviewed well by Hanson et al. . Kuzyakov  distinguished source of soil CO2 efflux in detail and evaluated the existing flux-partitioning approaches including root-exclusion, isotope-labeling, tree-girdling, component integration etc. All the approaches had intrinsic advantage and disadvantage, and no single, fully satisfactory flux partitioning method exist. In this study, we employed a variation of root exclusion technique called “root removal” coupled with chamber-based sampling because of its advantage in our main purpose, the long-term monitoring in natural environment.
 There are difficulties in the determination of the δ13C of soil-respired CO2 using chamber-based sampling. In the present paper, we have defined “soil-respired CO2” as that which diffuses across the soil–atmosphere interface and “soil CO2” as the CO2 found within the soil. Hereafter, we have abbreviated the δ13C of soil-respired CO2 as δ13CR-soil. The δ13CR-soil is controlled not only by CO2 produced within the soil but also by diffusion. Under steady-state conditions, δ13CR-soil equals the integrated value of the δ13C produced within the soil, but the δ13C of soil CO2 would be enriched by around 4.4‰ from the δ13CR-soil because of isotopic fractionation during diffusion [Amundsen et al., 1998]. Chamber-based measurements can lead to physical disturbance of the CO2 gradient at the soil–atmosphere interface and may thus produce artifacts in the estimation of soil CO2 efflux [Davidson et al., 2002] and thus, possibly in the estimation of δ13CR-soil. In particular, any pressure anomaly would cause mass flow of soil CO2 with an anomalously enriched δ13C value [Högberg et al., 2005]. This effect would lead to artifact in the δ13CR-soil determination. In addition, alteration of [CO2] in the chamber would change the [CO2] gradient at the soil surface. It would potentially affect the ratio of 13CO2 to 12CO2 that diffuse across the soil–atmosphere interface, but there is no theoretical analysis available for the effect presently. It should be noted that precise quantification of the magnitude of the bias in the δ13CR-soil resulted from the measurement artifacts was extremely difficult because of difficulties in accumulating sufficient information at specific times and locations (e.g., vertical distributions of the diffusion coefficient, in situ decomposition rates, and the isotopic composition of the decomposed material). Hence we must carefully plan the field-experiment.
 The potential problems in the previous sampling techniques had been pointed out in recent studies [e.g., Högberg et al., 2005; Mortazavi et al., 2004; Ohlsson et al., 2005]. Ohlsson et al.  tested two different sampling approaches with and without initial flushing of static closed-chamber interior with synthetic air that contained very low CO2. They reported that lowering of the initial CO2 fraction induced significant enrichment (>4‰) in the δ13CR-soil. As to the cause of the δ13CR-soil enrichment, the explanation was suggested that the initial lowering of the [CO2] caused a disturbance to the CO2 diffusion process within the soil-chamber system. Ohlsson et al.  also reported that the estimate of δ13CR-soil was not affected by the increase of [CO2] up to more than 2000 μmol·mol−1 for the non-flushed chamber though the apparent CO2 efflux in the chamber was significantly declined. The result suggested that the acceptable [CO2] range for the δ13CR-soil determination was larger than that for the determination of soil CO2 efflux.
Bowling et al.  and McDowell et al.  employed static closed chambers coupled with a flask sampling system for the δ13CR-soil estimation with consideration for measurement artifacts related to pressure anomaly and to [CO2] enrichment in the chamber headspace. The main concept of their experimental configuration was similar to our sampling system used in this study.
δ13CR-soil has been often estimated from vertical profiles of [CO2] and δ13C of soil CO2 [e.g., Mortazavi et al., 2004; Pendall et al., 2005]. This approach assumed that the respiratory end-member δ13C value was constant with depth. The profiles of soil CO2 and its δ13C were generated from samples collected below the surface soil layer. Hence the estimates by this approach would hardly include the influence of surface litter decomposition [Mortazavi et al., 2004]. Cisneros-Dozal et al.  suggested that leaf litter decomposition had large contributions to total soil CO2 efflux during the growing season, and that the decomposition rate was highly sensitive to the soil water contents, from the experiment using radiocarbon. In seasonal vegetation types like deciduous forest or in tropical ecosystem, decomposition of surface litter would be a key component to determine the seasonality of soil CO2 efflux and its δ13C. Therefore we considered that this soil-profile-based method was not appropriate for the objective of our study.
 In our field experiment, we employed a multichannel automated chamber system to continuously measure soil CO2 efflux, combined with a flask sampling system optimized for collecting soil-respired CO2 in this study. The chamber system had already been installed as part of a long-term soil-efflux monitoring study [Liang et al., 2003]. The dimensions of each chamber were 0.9 × 0.9 m, with a height of 0.5 m. The sampling area of each chamber was thus larger than that of previously described systems [e.g., Flanagan et al., 1996; Buchmann et al., 1997; Bowling et al., 2003; McDowell et al., 2004], and we predicted that this would help reduce the representation error that arises from small-scale spatial variability. The large volume, small vent, and slow movement of the pneumatically actuated lids effectively minimized pressure anomalies inside the chambers during their operation. The pressure fluctuation in the chamber was measured to be less than 0.22 Pa during regular CO2 efflux measurements [Liang et al., 2003].
 We designed the flask sampling system to collect air into a series of four flasks under positive pressure sequentially without introducing a pressure anomaly. For the flask sampling, the soil chamber was placed in series in a closed loop with a Mg(ClO4)2 (10–20 mesh, saturated with CO2, GFS Chemicals, Powell, OH) water trap, a diaphragm pump (Model-MOA, GAST Mfg., Inc., Benton Harbor, MI, USA), an assembly of four glass flasks (750-mL, each with two vacuum stopcocks with a Viton® O-ring seal at both ends; Koshin Rikagaku Seisakusho, Tokyo, Japan), a back-pressure regulator (Model-6800AL, KOFLOC, Tokyo, Japan), and a flow-meter (Model-RK1000, KOFLOC, Tokyo, Japan). All the glass flasks were connected in series. Solenoid valve arrays (USB3-6-2 and USG3-6-2, CKD, Tokyo, Japan) were placed in parallel with each flask to switch the flow path instantaneously between two modes, flow-through or bypass the flasks, without stopping the airstream. The details of the flask sampling system are described by Takahashi and Liang . Inflow to and outflow from the soil chamber were balanced throughout a sampling operation using this structure. Sample lines (Dekabon 1300, 6-mm outer diameter, 10 m in length, Nitta-Moore, Tokyo, Japan) were located between the sampling system and the chambers. The sampling system was covered with plastic box (dimension of basal plane was 0.75 m × 0.5 m) and was located on a wooden slatted drainboard more than 2 m apart from the nearest chamber. Hence the disturbance in soil CO2 efflux due to the covering of soil surface was unlikely. Efforts were made to avoid contaminating the atmosphere around the chambers with the CO2 contained in human breath.
 We collected air samples using the following procedure. To avoid contaminating the air around the chambers with air imported from outside the observation site, all flasks were evacuated before measurements began. About 5 min before closing the chamber lid, all flask stopcocks were opened, and all solenoid valves were set to flow-through the flasks. We then ran the pump to flush all the flasks and tubing with ambient air from the chamber; 5 sec after closing the lid of the chamber, an upstream solenoid valve array switched to bypass mode to isolate the flasks from the airstream, then stopcocks on both sides of the flask were closed. The other three flasks were isolated from the airstream and closed sequentially from upstream to downstream in the same manner at nearly constant time intervals. The air pressure inside the sampling system was kept constant (at approximately 100 kPa above ambient) by means of a back-pressure regulator. The flow rate of the sample air was about 6 L·min−1 during the sampling. Overall collection times were shorter than 810 sec.
 We ascertained that fluctuation in pressure of chamber-headspace appeared during the switching of the flow-path in the sampling operation. Hence measurement artifacts related to pressure anomaly was supposedly negligible in our measurements. To assess the influence of enrichment of [CO2] in the chamber headspace, we tested consistency of the [CO2] increasing rate in unit time and linearity between δ13C and 1/[CO2] for all the sampling that we conducted. The maximum range of CO2 in the chamber headspace from start to end of sampling was about 250 μmol·mol−1. Although the increasing rate of [CO2] significantly declined as the [CO2] enriched, we could not found evidence of the influence of the [CO2] enrichment on the linearity between δ13C and 1/[CO2] [Takahashi and Liang, 2008]. R2 for the δ13C-vs-1/[CO2] relationship was never to be less than 0.995 and no systematic tendency was found in all the measurements. To our results, the estimates of the δ13CR-soil were rather insusceptible to the influence of the CO2 enrichment in the chambers.
2.3. Root Exclusion
 To observe variations in the δ13C of heterotrophic respiration under field conditions, we excluded roots by means of a method called “root removal” [Hanson et al., 2000]. In June 2002, roots in five plots were carefully removed from the soil in 1.0 × 1.0 m areas to a depth of 30 cm, then the soil was returned to each pit with its original orientation preserved. Invasion of roots was prevented using vertical physical barriers made from polyvinylchloride boards on each side of the pits. The basal plane of the pits was not covered with these barriers. A lack of uniformity in belowground CO2 production might have produced gradients in soil CO2 and consequently caused lateral diffusion below the barriers. At this site, the soil layer was only 10 to 15 cm thick and the roots spread almost exclusively above a depth of 20 cm. Under those conditions, belowground CO2 production would be concentrated within the soil above the basal plane of the barriers. The vertical CO2 gradient above the basal plane would be steeper than the lateral gradient below the plane, lateral diffusion within the soil is unlikely to have been significant. Therefore, we have assumed that any CO2 that invaded the chamber from outside the barrier as a result of lateral diffusion would have only a minor contribution to the CO2 efflux observed in the root-exclusion plots.
 The possible disturbance of heterotrophic respiration caused by root removal was summarized by Hanson et al. . This technique would result in an initial flush of CO2 out of the soil following disturbance. Time must pass for the increased CO2 production rate to subside, and to allow time for the diffusion rates and production rates of CO2 to come back to equilibrium. However, they argued that root exclusion studies are most useful if the measurements extend through a complete annual cycle. For a study with the objective of observing seasonal or longer-term variations in heterotrophic respiration, elimination of the contribution from turnover of the belowground litter caused by using this method was not possible, but we consider the resulting bias to be acceptably small.
 For the observations in 2002, it is possible that the impact of the physical disturbance created by removal of the roots had not yet disappeared. Hence, we caution readers that the δ13C seasonality observed in 2002 may be misleading. However, given the small magnitude of the disruption predicted by the results of Hanson et al.  and the lack of any obvious difference between the 2002 response patterns and those in 2003 and 2004, we feel that the 2002 results are nonetheless useful in terms of the pattern, if not the magnitude, of the variation.
2.4. Laboratory Analysis
 We analyzed the [CO2] and the δ13C of the CO2 in the air samples collected at the study site in a laboratory of the National Institute for Environmental Studies. The [CO2] values in the samples were determined using a nondispersive IRGA (LI-6252, LI-COR, Lincoln, NE, USA) and were compared with our laboratory's CO2 standard scale (the NIES95 scale) prepared using a gravimetric method. Our NIES95 scale was compared with a standard CO2 scale provided by the Climate Monitoring and Diagnostics Laboratory of the National Oceanic and Atmospheric Administration (NOAA/CMDL) in 1996. Differences in [CO2] between the two laboratories were less than 0.12 μmol mol−1 for a range of values from 343 to 373 μmol mol−1. The precision of the [CO2] analysis in the present study was estimated to be better than 0.10 μmol mol−1 based on replicated analysis and storing test for 1-week. After analyses of [CO2] and other gas components ([CH4], [N2O], [CO], [H2], [SF6] and O2/N2 ratio), we performed cryogenic extraction of CO2 for our isotopic measurement using a glass vacuum line. The principle of this extraction is similar to that described by Vaughn et al. .
 Determination of δ13C was also performed at the National Institute for Environmental Studies. The extracted CO2 was introduced into an isotope-ratio mass spectrometer (IRMS; Delta-PLUS, Thermo Electron Co., Waltham, MA, USA) using variable-volume, dual-inlet devices. We corrected for the presence of N2O in the sample CO2 using measured [N2O]/[CO2] values for each sample and a correction factor that accounted for differences in ionization efficiency between CO2 and N2O according to the concept of Friedli and Siegenthaler .
 The carbon stable isotope ratio (delta notation) was defined as follows:
As for the stable isotope ratio of carbon, values were reported using the Vienna-PDB scale. The overall precision of the δ13C analysis (including the CO2 extraction process) was estimated to be better than 0.02‰ by replicated analysis and storing test (1 week). We also tested that [CO2] and δ13C was not affected by passing through the Mg(ClO4)4 dryer as far as the deliquescence of the reagent did not occurs.
2.5. Determination of δ13C of Soil-Respired CO2 Using the Keeling Plot Approach
 To determine the δ13CR-soil value, we used a two-component simple mixing model called the “Keeling plot approach” [Keeling, 1958]. The usability and limitations of the Keeling plot approach were described in detail by Pataki et al. . In this study, we assumed that the relationship between [CO2] and δ13C in the chambers was expressed by the following equation:
where the subscripts Ch and BG represent the atmosphere in the chambers and the background atmosphere, respectively. Assuming that there are no changes in both δ13CBG and δ13CR-soil between the start and end of each sampling period, the intercept of the linear regression of δ13C versus 1/[CO2] observed in the chamber represents the δ13CR-soil. We used Model I (ordinary least squares) regressions to determine δ13CR-soil according to the recommendation in Zobitz et al. .
 As we mentioned above, the potential influence of the [CO2] enrichment was unavoidable in the chamber-based sampling sampling. While collecting samples with wider [CO2] range contributes to minimize standard error of δ13CR-soil, it raises the risk of potential influence related to the [CO2] enrichment. To our results, the estimates of the δ13CR-soil were rather insusceptible to the influence of the [CO2] enrichment (up to c.a 250 mmol mol−1, we tested) in the chamber as compared with the soil CO2 efflux [Takahashi and Liang, 2008]. This result was consistent with the finding of Ohlsson et al. .
 High-precision isotope measurement coupled with a sampling system optimized for soil respiration allowed us to capture the variability in δ13C of soil-respired CO2 under natural conditions.
3. Results and Discussion
3.1. Possible Causes of Representation Error With Chamber-Based Measurements
 To obtain valid estimates of isotopic disequilibrium between the atmosphere and the terrestrial biosphere and of seasonality in δ13CR-soil, measurements of δ13CR-soil must be unbiased when compared with a representative value for appropriate spatial scales and timescales. “Snapshots” of these values obtained using a chamber-based sampling method would be representative for a spatial scale of approximately 0.8 m2 and a timescale of several minutes. In terms of the objective spatial scale, we should attempt to estimate representative values for the stand-scale or larger. With a limited number of observations in chamber-based sampling, spatial heterogeneity in δ13CR-soil might lead to a serious representation error due to sampling bias. Large spatial variability in soil CO2 efflux is a common phenomenon [e.g., Liang et al., 2004; Søe and Buchmann, 2005] and it was predicted to be found also in the δ13CR-soil. Before discussing the seasonal variation in δ13CR-soil or in the isotopic disequilibrium, we examine the short-term temporal variability and the spatial heterogeneity in δ13CR-soil.
3.1.1. Short-Term Variations in δ13C of Soil-Respired CO2
 To illustrate the short-term variability in δ13CR-soil, we brought forward the cases that the sampling was conducted for two or more consecutive days. In Figure 3, we showed soil temperature, volumetric soil water content, soil CO2 efflux and δ13CR-soil observed for the cases at a root-exclusion plot (chamber 3) and a non-root exclusion plot (chamber 10). In most cases ((b), (c), (d), (e), the second and the third data in (g), (h), (i) and (j)), the sampling was conducted in sequence, on an afternoon and then on next morning. The time periods corresponded nearly to that maximum and minimum of the soil temperature appeared in diurnal variation, respectively. The results from the root-exclusion plot (open circles) has remarkable feature that the change in the δ13CR-soil was inversely correlative to the change in the soil CO2 efflux in all the cases except for (a) and (j). This correlative changes suggest that there is temperature-associated controlling factors on those short-term variations common to both the soil CO2 efflux and the δ13CR-soil.
 In second data points of case (a), δ13CR-soil at root-exclusion plot showed significant enrichment as the soil CO2 efflux increased during a rapid rise of soil water content without significant changes of soil temperature. This anomalistic feature is most likely due to the extrusion of 13C-enriched soil CO2 by rainfall-induced change in soil water content. We cannot find reasonable explanation for the exceptional tendency in δ13CR-soil found in case (j).
 As for the short-term variations of soil CO2 efflux in forest ecosystem, number of field-based studies has been published. Tang et al.  reported that the soil CO2 efflux exhibits significant diurnal variations associated with soil temperature. They suggested that the short-term variations in soil temperature might affect CO2 efflux by changing the diffusion velocity near the air–soil interface and by the effects on microbial activity. Gaumont-Guay et al.  investigated the seasonal and diurnal dependence of soil CO2 efflux on soil temperature and soil water content based on the continuous half-hourly measurements of soil CO2 efflux in a boreal forest. Their results suggested that the change of the vertical distribution of soil CO2 production would have influence on temporal variations of soil CO2 efflux. The change of the vertical distribution of soil CO2 production was important factor to interpret the short-term variations of the δ13CR-soil observed in the root-exclusion plot. It has been commonly observed that δ13C of soil organic matter become less depleted in greater depth in soil profile [e.g., Ehleringer et al., 2000; Bowling et al., 2002]. Soil in shallower depth exhibited diurnal temperature variation with greater amplitude. The change of temperature profile involve the change in vertical distribution of soil CO2 production because decomposition rate of soil organic matter has significant temperature dependence, i.e., soil CO2 production in the shallower depth is affected from greater soil temperature variation than in the deeper depth. Relative contribution of CO2 produced in the shallower depth was to be greater in high-temperature time, and lesser in low-temperature time in the diurnal cycle. Assuming that the CO2 produced in shallower depth had more depleted δ13C than in greater depth, the δ13CR-soil should be more depleted in high-temperature time, and less depleted in low temperature-time. This hypothesis can provide a reasonable explanation for the observed short-term variation of the δ13CR-soil in the root-exclusion plot. But it should be noticed that we could not find quantitative relationship between the soil temperature gradient and the observed δ13CR-soil (we did not indicate in figure). The seasonal or long-term variations in the δ13CR-soil were not explicable solely by the effect of the change in the vertical distributions of soil CO2 production.
 Temporal variations in soil CO2 efflux are generally attributed also to change in soil water content [e.g., Davidson et al., 1998; Gaumont-Guay et al., 2006]. However, there was no evidence for seasonal drought at this site, because rainfall usually occurred once or twice a week. Abundant precipitation at our study site, coupled with good soil drainage, resulted in a volumetric soil water content, usually 30–40%, that was uniformly favorable to microbial activity throughout the growing season [Liang et al., 2004]. Hence we considered that influence of soil water content was significant.
 Comparison of the result from the non-root-exclusion plot (crosses in the figures) with the root-exclusion plot (open circles) provided additional information on variation in δ13CR-soil. The perturbations in CO2 transport process at air-soil interface by changes in physical factors (i.e., temperature and rain pulse) should affect δ13CR-soil in a same sense for both the plots, with or without root-exclusion. In all cases except for (a), (b) and (g), tendency of the change in δ13CR-soil observed at the non-root-exclusion plot followed the tendency found at the root-exclusion plot in varying degrees. However, in cases (a), (b) and (g), δ13CR-soil at the non-root-exclusion plot showed tendency different from that at the root-exclusion plot. Those anomalous variations in the non-root-exclusion plot might reflect the change in photosynthetic isotope discrimination via root respired CO2 because all the cases were in the growing season of the forest. Tang et al.  found that tree photosynthesis modulates soil CO2 efflux on a diurnal timescale. We suppose that higher supply of photosynthate from leaves to root in the season likely fluctuate the δ13CR-soil.
 In our results, the range of short-term (<24 h) temporal changes in δ13CR-soil reached 0.73‰ in 5–6 December, 2002 (case (e)) and 0.65‰ in 13–14 November, 2003 (case (j)). It seems that the magnitude of the short-term variation become greater in colder period except for the case of rainfall (case (a)). We could not clarify the factors that determine the magnitude of the short-term change from existing information. The short-term variations in the δ13CR-soil provide representation error in analyses of long-term temporal variation and of spatial variation. To reduce the representation error, averaging of data observed in different time in the day would be effective means. Therefore, in the discussion of seasonal variations of the δ13CR-soil in later section, we used flux weighted mean values of the δ13CR-soil for the cases that multiple sampling was conducted in short period of time (i.e., the cases shown in Figure 3).
3.1.2. Spatial Variation in the δ13C of Soil-Respired CO2
 Although the study site was in an artificial forest and, consequently, was more uniform than a natural forest in many of the forest's properties (e.g., tree species, ages, and dimensions, as well as stand density), the forest floor was still heterogeneous at the spatial scale of the sampling chambers (∼0.8 m2). To test the spatial variability and representativeness of the δ13CR-soil values measured using the chambers, we collected samples using 10 chambers in different plots (five in the root-exclusion plots and five in non-root-exclusion plots) on 30 June and 27 August 2004 (Figure 4). The arrows in the figure denote the direction of the change from early to late summer. It was obvious that δ13CR-soil had high spatial variability in both the root-exclusion and non-root-exclusion groups at both times of year. The δ13C value varied with the range larger than 2‰ in both treatment groups at both times of year. The significant spatial variability in the root-exclusion plots suggested that some factors intrinsic to heterotrophic respiration must be responsible for the observed variability in δ13CR-soil.
 A possible cause of this variability would be a lack of uniformity in the organic matter being decomposed at different locations. As mentioned previously, there were significant differences in δ13C of the leaves of the different tree species at our study site. Variability in the relative contributions of these respiration substrates of different origin should be reflected in the heterogeneity of the mean δ13C in the chambers. In addition, small-scale heterogeneity in the soil environment, such as differences in soil temperature and soil moisture, would also contribute to the spatial variability in δ13CR-soil. Soil organic matter is composed of a range of compounds with different chemical forms, decomposition rates, and isotopic compositions [e.g., Gleixner, 2005]. This environmental heterogeneity might have caused the differences in the decomposition rates of individual substrates, which would consequently be reflected in the δ13CR-soil variability.
where n is the sample number requirement, t the t-statistics for a given confidence level and degrees of freedom, s the standard deviation of the full population of measurements, an range the width of the desired interval about the full population mean in which a smaller sample mean is expected to fall. According to this equation, in our study site, ±20% precision with 95% confidence interval for the soil CO2 efflux would be achieved by five sampling point with our chamber system [Liang et al., 2004]. We calculated the number of sampling points required for determination of δ13CR-soil at the root-exclusion plot based on the data observed at 30 June 2004 (number of points was 5, mean was −28.91‰ and standard deviation was 1.43‰). The results demonstrate that 64, 254, and 6328 points are required to obtain an experimental mean within ±1‰, ±0.5‰ and ±0.1‰, respectively, with 95% confidence interval.
 At least at this study site, the representation error caused by the spatial variation in δ13CR-soil made it extremely difficult to determine the representative δ13CR-soil at the stand-scale or larger within an uncertainty of required level for validating modeled isotope disequilibrium (<1‰ as global mean) based on a feasible number of chamber-based measurements. Under these circumstances, we had to leave the observational validation of isotope disequilibrium between the soil and the atmosphere for future research.
 As for the soil CO2 efflux, its significant spatial variability under natural environment are well known, but a lot remains to be established about factors that control the variation [e.g., Davidson et al., 1998; Buchmann, 2000; Xu and Qi, 2001]. Søe and Buchmann  investigated the spatial variations in soil CO2 efflux and its controlling factors in an unmanaged beech forest. Their results showed that spatial patterns of the soil CO2 efflux was fairly stable throughout the growing season and was closely related to stand structure of the forest. This suggested that the spatial variation in the soil CO2 efflux was largely controlled by direct and indirect influence from living plants. However, our results showed that the spatial pattern of the δ13CR-soil at non root-exclusion plots varies significantly between two observation periods in the growing season. This indicates that the spatial variations of the δ13CR-soil cannot be explicable directly from stand structure, even though root respiration had large contribution on the total soil CO2 efflux. δ13C of root respiration likely reflect the photosynthetic isotope discrimination of the plant [Ekblad and Högberg, 2001]. The photosynthetic isotope discrimination alters with environmental factors (availabilities of water, light, etc.) and physiological characteristics of plant leaves. In deciduous vegetation, adding to the short-term variations in environmental factors, the light availability for individual trees likely varies with seasonal changes of canopy structure. Furthermore, enzymatic CO2 fixation efficiency of the leaves might have seasonal variation due to the plant phenology. Hence the δ13C of root respired CO2 likely have significant short-term and long-term variability specific to each individual locations. Consequently, its spatial pattern possibly has temporal variability.
 As for the situation in the absence of influence of living root, we found an interesting feature in the results shown in Figure 4. The value of δ13CR-soil tended to increase from July to August 2004 in all five plots in the absence of root respiration. In contrast, there was no common trend in the plots without root-exclusion. Even though the magnitude of this increase was anomalously large in the summer of 2004, a similar trend was found in the regular measurements in 2002 and 2003 at a root-exclusion plot (chamber 3; see section 3.2). Based on these results, we believe that it is possible to capture meaningful profiles of temporal variation in the δ13C of heterotrophic respiration by means of regular, fixed-point observations of δ13CR-soil in the absence of root respiration.
3.2. Seasonal Variability in the δ13C of Soil-Respired CO2
Figure 5 presents time series of δ13CR-soil observed by means of regular measurements at two fixed plots with root-exclusion (chamber 3) and without root-exclusion (chamber 10), along with the simultaneous changes in soil temperature and soil CO2 efflux. The values of soil CO2 efflux in this figure were calculated from the [CO2] in the flask samples. We use the CO2 efflux values calculated from flask measurements, not from IRGA-measurement, to avoid introducing inconsistency due to the absence of some part of corresponding raw IRGA data recorded on-site has been uncollectible by some hardware accidents like lightning damage.
 In some sampling periods, we conducted multiple within 24 hours. We can find short-term changes in δ13CR-soil even in both plots with and without root-exclusion. The changes cannot be explicable only by contribution of root respired component. We supposed that the short-term variations in δ13CR-soil were associated with fluctuations in physical factors such as soil temperature and soil water content. Future work should address controls on the short-term δ13CR-soil variations. As we mentioned above, the range of short-term (<24 h) temporal changes in δ13CR-soil reached a maximum of more than 0.70‰. This magnitude in the short-term δ13CR-soil variations was not negligible compared with the seasonal δ13CR-soil. However, the representation error caused by the short-term variation was effectively cancelled by the averaging of the data in many observation periods in our study. Hence we consider that the short-term δ13CR-soil variations would not affect decisively the interpretation of the seasonal variations.
 An important feature of this data was that the δ13CR-soil exhibited significant seasonal variability even in the absence of root respiration. The δ13CR-soil was generally lower in summer and higher in autumn and spring. In each year, the difference between the highest and lowest δ13CR-soil value was greater than 1‰. The amplitude of the seasonal variation in δ13CR-soil was thus larger than the sampling bias that resulted from short-term variations in δ13CR-soil (∼0.50‰ in our experience, as described previously). In addition, the trend in the temporal variation in δ13CR-soil observed in the plots with and without root-exclusion (chamber 10) was similar. The variation in δ13CR-soil should thus be largely caused by changes in the δ13C of the heterotrophic component of soil respiration. The lack of stand-scale representativeness of the δ13CR-soil values prevented us from quantifying the contribution of root (or heterotrophic) respiration to the overall δ13CR-soil variation using 13C mass-balance equations based on the difference between chambers 3 (root exclusion) and 10 (no root exclusion). Hence, we do not discuss the contribution of root respiration to the variability in δ13CR-soil in this study.
 In general, the variation in soil CO2 efflux is closely associated with changes in soil temperature and soil moisture. At our study site, soil CO2 efflux was not regulated by a lack of soil moisture because there was frequent rainfall during the study period [Liang et al., 2004]. Therefore, we will not discuss the influence of soil moisture. Instead, we tested the temperature dependencies of soil CO2 efflux and of δ13CR-soil, and their seasonal changes in the root-exclusion plot (chamber 3; Figure 6). Because the observations during 2002 and 2004 covered only half of the non-snow-covered period in these years, we have only shown the results during 2003. In Figures 6b and 6d, we used the data averaged for some sampling periods to reduce the representation error caused by short-term variations. The soil CO2 efflux showed a clear exponential increase with increasing soil temperature. Soil CO2 efflux during the progression of the seasons followed the same monotonic exponential curve, increasing as temperatures increased then decreasing again as temperatures decreased, with no evidence of hysteresis. In contrast, the relationship between δ13CR-soil and temperature followed no clear pattern, other than having an overall negative correlation. The sampling bias induced by the observed short-term variations in δ13CR-soil might be partially responsible for this seeming lack of a temperature dependency. However, the magnitude of the seasonal change in δ13CR-soil was still significant and meaningful. The value of δ13CR-soil formed a closed, ladle-shaped curve with the following seasonal course: (i) From spring (140 DOY) to summer (196 DOY), δ13CR-soil decreased, reaching its minimum value (196 DOY; Figure 6d) before soil temperature reached its maximum value (230 to 233 DOY; Figure 10b). (ii) From early summer to early autumn (starting at 167 to 170 DOY and ending at 260 to 261 DOY), δ13CR-soil increased independently of the change in soil temperature. (iii) From autumn (260 to 261 DOY) to winter (316 to 317 DOY), δ13CR-soil initially decreased to a local minimum (at 295 to 296 DOY), then increased to its maximum (316 to 317 DOY) thereafter. This local minimum corresponded to the time of maximum litterfall (Figure 2). The decrease in δ13CR-soil from spring to summer was also observed in 2004 and the summer increase in δ13CR-soil was also found in 2002 and 2004 (Figure 5).
 These features suggest that the seasonality in δ13CR-soil could not be explained by means of a simple analogy with the soil CO2 efflux. Changes in the quality of the decomposing soil organic matter could be a key factor in regulating the seasonal course of variations in δ13C in heterotrophic respiration. Soil organic matter is composed of various carbon pools with different chemical forms, decomposition rates, and isotopic compositions [e.g., Gleixner, 2005]. In models [Fung et al., 1997; Randerson et al., 2002], the 13C flux from heterotrophic respiration has been expressed as a composite value for these different compartments. Andrews et al.  found the significant shift in δ13C of CO2 evolved from root-free soil with magnitude of about 2‰ in their 32-days incubation experiments. The shift was likely due to the decay of labile soil organic matter pool. In their study, root exudates and root detritus were supposed to be sources of the labile substrates. We consider that similar shift in δ13CR-soil might occur due to the decay of labile substrate in fresh leaf litter even in the absence of living roots.
 The seasonal variation in the δ13C of heterotrophic respiration reflects the change in the relative composition of the flux components from the individual compartments. We hypothesize that the seasonality in the input and subsequent decomposition of leaf litter influenced this variation. The leaves of the larch and of the mixed broadleaved trees at our study site had a lower δ13C value than the bulk organic matter in the surface soil, which suggests that the newly deposited leaf litter included a rapidly decomposing substrate with a lower δ13C value and a slow-decomposing substrate with a higher δ13C value. The CO2 that originated from the bulk leaf litter should gradually become 13C-enriched as decomposition progresses.
3.3. Simulation of the δ13C Seasonality Using a Simple Two-Compartment Model
 In this section, we illustrate the factors that contribute to the general characteristics of the observed seasonality in δ13C of heterotrophic respiration. First, in general, the δ13C of heterotrophic respiration was negatively correlated with the seasonal changes in soil temperature. Second, the seasonal course of the δ13C of heterotrophic respiration formed a closed, ladle-shaped trajectory in the graph of δ13C versus temperature (Figure 6d). We hypothesized that the former characteristic was mainly caused by differences in the temperature dependence of decomposition rates between the individual compartments of the carbon pool and that the latter characteristic was related to decay of the more labile 13C-depleted substrate as decomposition progressed.
 We tested these hypotheses by means of a simulation that was based on a simple two-compartment (labile and slow-decaying organic matter) model. The main purpose of this test was to help us understand how the general characteristics of the δ13C seasonality developed rather than to analyze them quantitatively. Assuming that the two individual compartments in the soil carbon system had unique temperature dependencies of their respective decomposition rates, we expressed the heterotrophic respiration (Rh) by a modified equation based on equation (4) in Randerson et al. , as follows:
where k(i) is the decomposition rate constant for pool i, C is the temporally varying carbon content of each pool, Q10(i) represents the change in decomposition rate per 10°C change in temperature [Fang and Moncrieff, 2001], T(t) is the soil temperature at time t, and Tref is the reference soil temperature on which Q10 is calculated. To simplify the equation, we substituted Rref(i, t) for k(i)C(i, t).
where Rref represents the respiration rate at reference temperature Tref. Since k(i) is a constant, Rref(i, t) for each pool (i) is proportional to C(i, t). Assuming that there is no isotopic fractionation during decomposition, the δ13C of the CO2 that originated from each compartment equals the δ13C of the carbon in the compartment. Introducing δ13C into the equation, we obtain:
where δ13CRh is the δ13C value for overall Rh and δ13C(i) is the δ13C of carbon in each compartment and the CO2 that originated in the compartment. For simplicity, we have assumed that Rh consists of two compartments (i.e., n = 2 in equations (4), (5), and (6)): one with a larger contribution to soil CO2 efflux and with a higher δ13C (hereafter denoted by A), and another with a smaller contribution to the efflux and with a lower δ13C (denoted by B). In this calculation, we used monthly mean soil temperature at a depth of 5 cm in 2003 as T(t) in these equations and defined Tref as 0°C. The time step used in this calculation was 1 month. In this situation, t corresponds to individual months. The respiratory flux from component i in month t would thus be expressed as follows:
The sum of the CO2 respired from both compartments during the course of a year was normalized to a value of 1, and Rref(i, t) for individual compartments was calculated with respect to this normalized value to give the relative contributions from compartments A and B to the annual flux of 80 and 20%, respectively. Thus:
 We set the annual mean flux value of the δ13C of respired CO2 to be −26.7‰ PDB based on the flux-weighted mean value of the δ13C observed in 2003. Then the δ13C(i) for compartment A was set to −26.0‰ PDB from the least depleted δ13C value observed in 2003. Because this value should represent the situation that contribution from the compartment B was minimum. The value was the lower limit of the δ13C assumable for the compartment A. Finally, the δ13C(i) for compartment B was set to −29.5‰ PDB from mass balance. (The δ13C(i) for compartment B was basically linked to the choice of the assumed relative contributions from each compartment in total CO2 efflux. For example, if we set relative contribution from compartment B in the total CO2 efflux to be 10% instead, the δ13C(i) for compartment B was to be −33‰ PDB.) As we mentioned above, the leaves of larch, which was the dominant tree species of the site, had δ13C value of about −29.7‰ PDB and degraded organic matter in the soil surface had less depleted δ13C value than that. This involved that δ13C of CO2 evolved from degraded leaf litter was more depleted than the δ13C of the living leaves, −29.7‰ PDB. Therefore the value of δ13C(i) for compartment B, −29.5‰ PDB, is reasonable, although it is significantly lower than the most depleted δ13CR-soil value observed in 2003.
 First, we examined the influence of different temperature dependencies (Q10(i) in equations (4)–(6)) on the δ13C seasonality and its temperature relationship under the hypothetical condition that the pool size (C(i, t) in equation (4)) for the individual compartments remained constant over time. (Based on this condition, Rref(i, t) was also constant with time.) Assuming a constant size of the individual compartments, which was the basic assumption in this test calculation, assumes an unrealistic condition in which carbon loss via respiration is compensated for by litter input at all times or that the carbon pool sizes for both compartments were infinitely larger than the carbon loss via respiration. Nonetheless, this approach permits a qualitative investigation of general trends in δ13C seasonality. We compared the results obtained from three different combinations of temperature dependence (Figure 7): Q10(A) = Q10(B), Q10(A) > Q10(B), and Q10(A) < Q10(B). We chose 1.5 for the Q10(A) value based on the rough estimates from soil CO2 efflux observed in 2003 (Figure 6a). It should be noted that, because the number of the data points used in the Q10 determination is fairly small, the Q10 value probably contains large uncertainty. We set the Q10(B) value to be 1.0, 1.5 and 2.0, respectively, without concrete motive. It should be noted that factors other than magnitude relation of the Q10 values between the two compartments had no critical influence on conclusion of this calculation. When compartments A and B had the same Q10 value, δ13CRh showed no variation with time even though Rh showed clear seasonal variation. This occurred because there was no temporal variation in the relative contribution of the two compartments to Rh. When Q10 was larger for compartment B than for compartment A, the larger contribution from compartment B decreased δ13CRh during the summer. This suggests that the decreased δ13CRh in summer could be explained by the different temperature dependence of decomposition in the two compartments. However, under the assumption of a constant carbon pool size, the temperature dependence of δ13CRh showed a monotonic exponential change as a function of soil temperature that was dissimilar from the observational results.
 Second, to illustrate differences in seasonal trends in the temperature dependencies of Rh and δ13CRh, we introduced terms for the decay of the labile compartment into the model, because the decay of the carbon pool is an important factor that regulates the seasonality of Rh [Randerson et al., 1996]. At our study site, leaf litter input into the soil carbon pool was concentrated in October and November. Hence, we made the basic assumption that the labile compartment with decreased δ13C (compartment B in this calculation) was input into the soil system simultaneously as leaf litter at the beginning of November, and decomposed gradually during the following 12 months until the next input was supplied in the following November. In this situation, November represents the initial month (t = 1) in the model's 12-month sequence. The rate of decomposition was assumed to be regulated by the monthly mean soil temperature and by Q10(i), as follows:
 To express the seasonal decrease in compartment size, we introduced the parameter Dd, which is defined as the ratio of the carbon decomposed during the 12-month period to the initial carbon abundance in compartment B just after the initial loading of leaf litter:
When Q10(B) and Dd are given, the ratio of C(B, 1) to C(A) can be identified uniquely. Consequently, values of R(B, t) for the 12-month period can be determined. We can then calculate seasonal changes in Rh, the relative contribution of compartment B to Rh and δ13CRh, and the temperature dependencies of Rh and δ13CRh for different values of Dd. When we assume the same Q10 values for both compartments, Q10(A) = Q10(B), the seasonality of δ13CRh is defined by the change in the ratio of the pool sizes of the two compartments. Under this condition, δ13CRh decreased unidirectionally as the decay of compartment B progresses during the 12 months after the input of leaf litter. This suggests that the assumption of Q10(A) = Q10(B) cannot explain the summer minimum for δ13CRh. Figure 8 shows the results of our simulation under three different set of values for Q10(A), Q10(B), and Dd: (i) Q10(A) = 1.5, Q10(B) = 2.0, and Dd = 0.50 (solid squares); (ii) Q10(A) = 1.5, Q10(B) = 2.0, and Dd = 0.90 (open circles); and (iii) Q10(A) = 1.5, Q10(B) = 5.0, and Dd = 0.90 (crosses).
 Introduction of the decay in carbon pool size in compartment B led to a gap in the seasonal variation of the relative contribution of compartment B, Rh, and δ13CRh between 2 months before and after the input of leaf litter. Compared with the relative contribution of compartment B and of δ13CRh, the gap in Rh was relatively small because the seasonality in Rh was bounded mainly by the contribution of compartment A, which was assumed to have constant size. When we compared cases (i) and (ii), the gap in δ13CRh during the litter-input period was greater for the larger Dd value. In case (ii), the increasing trend from the litter-loading period dominated the temperature-associated variation in the δ13CRh seasonality. The results of case (i) suggested that seasonal changes in the carbon pool size of compartment B explained the timing of the summer minimum of δ13CRh. The δ13CRh reached its minimum in June, which was earlier than the period of maximum soil temperature (August). However, using the Q10 values we assumed in cases (i) and (ii), a prominent decrease of δ13CRh and an increase in Rh appeared during the period of litter input. This change seemed to be larger than the observational results. We hypothesize that the low temperature during in the litter-input period suppressed the activity of the microbial community responsible for decomposition of the labile substrate (compartment B in this test calculation) under natural conditions. This situation can be expressed by using a greater temperature dependence for compartment B (Q10(B)) in this calculation. The effect of different Q10(B) is illustrated by comparing cases (ii) and (iii). Using a Q10(B) value that was drastically larger than Q10(A) led to rapid decomposition of the carbon pool in compartment B during the high-temperature period. Consequently, this change suppressed the δ13CRh decrease after the litter input and emphasized the summer δ13CRh decrease. Consequently, the time series for δ13CRh showed clear differences between the summer and other seasons, with a significantly large amplitude. In case (iii), the seasonal course of δ13CRh in the δ13C-versus-temperature diagram (Figure 8e) formed a closed, ladle-shaped trajectory. This drastically high Q10 value may be caused by a phenological change in the population of microbes responsible for decomposition of the labile organic matter in the leaf litter. Nonuniformity in soil temperature also may have influence on the high Q10 value. The soil surface temperature likely had seasonal variation with greater magnitude than that in 5cm depth, which was used in our simulation. Hence the labile component in the litter in the soil surface should be affected by greater seasonal temperature change under the natural environment than under the condition we assumed in the calculation.
 We notice here the influence of the choice of assumed values except for Q10 on the results. As we mentioned above, the δ13C for compartment B is linked to the relative contributions of compartment B on the total CO2 efflux in our determination procedure of the values. If we are to assume the higher δ13C for compartment B, the relative contributions of the compartment B must be enlarged. Choice of the assumed values for the δ13C and the relative contribution of compartment B likely affect the seasonal course of the soil CO2 efflux, but not the course of the δ13CRh significantly. This is because the effects from the lowered (or raised) δ13C for compartment B and from the increased (or reduced) contribution of compartment B are compensative each other in the simulated seasonal course of the δ13CRh. On the other hand, the increasing of the contribution of compartment B poses a larger hysteresis in the seasonal course of temperature relationship of the soil CO2 efflux according to the enlarged influence from the seasonal decay of pool size of compartment B.
 Difference in temperature dependence of the decomposition rate of organic matter among different soil carbon pools have been a topic of debate in the context of global warming. Liski et al.  observed decomposition rate of old organic matter to be insensitive to temperature. Analysis of Giardina and Ryan  suggested that the decomposition rate of organic carbon in forest mineral soil is not controlled by temperature limitation to microbial activity. Those field-based studies argued that older carbon pools should have less temperature dependence in the decomposition. On the contrary, recent studies based on incubation experiment demonstrated that the temperature dependence would not vary with the age of carbon pools [Fang et al., 2005; Reichstein et al., 2005]. The focal point of those studies is to ascertain whether there exists significant difference in temperature dependence of the decomposition rate between in soil organic layer and in mineral soil. It should be noted that our discussion about the potential nonuniformity of the Q10 is directed to the processes in soil carbon pools with very short turnover time. Hence our findings in this study would hardly have important implications for the studies in the context of global warming because of discrepancy in subjected timescale.
 In summary, the simple two-compartment calculation illustrated that accounting for a combination of three key factors (a large intercompartment difference in δ13C, seasonal changes in the size of the labile compartment associated with input and decomposition of leaf litter, and a drastically greater Q10 value for the labile compartment) can simulate three notable characteristics found in our 2003 observations: (1) obvious seasonality that involves a summertime decrease in δ13CRh, (2) the appearance of the δ13CRh minimum in advance of the soil temperature maximum, and (3) a local minimum of δ13CRh during the period of concentrated litterfall.
 The ladle-shaped seasonal course of δ13CRh in the diagram of δ13C versus temperature (Figure 8e) was demonstrated by simulating the interplay of the abovementioned factors and appears to be a necessary result, even though it seemed odd at first glance. However, some points of difference remain between the simulated and observational results, such as the findings that the temperature dependency of Rh showed a distorted loop when we introduced a seasonal change in the pool size and that the obvious maximum for δ13CRh appeared just before the period of litter input. The former observation suggests that the labile organic matter (compartment B in the simulation) contributed less (ca. 20%) to Rh than was assumed in the simulation. The second observation was likely modified by assuming a slower rate of decay of the labile organic matter than that assumed in the simulation (Dd = 0.90). If our hypothesis is correct that the labile organic matter, with highly decreased δ13C, has a high temperature dependence (Q10), then the seasonal transition in δ13CRh should be deeply influenced by anomalous soil temperatures during the high-temperature season because the decay of the labile substrate depends strongly on temperature. This hypothesis effectively explained the extreme increase of δ13CR-soil that we observed in August 2004. The soil temperature at a depth of 5 cm in 2004 was 2.2°C higher in July and 0.5°C higher in August than the temperatures in 2003. These high temperatures might have caused rapid depletion of the labile organic matter, consequently producing an anomalous increase in δ13CR-soil in late August 2004. It should be noted that the high temperature dependence of the decomposition rate of the labile substrate leads to significant year-to-year variation in the seasonality of δ13CR-soil.
 We predicted that many factors of the seasonality in δ13CR-soil that we have discussed would be strongly associated with the strong seasonality of litterfall in this vegetation type (a deciduous needle-leaf forest). The seasonality in an evergreen needle-leaf forest, which is a dominant vegetation type in high-latitude forests of North America and northwestern Eurasia, can be expected to be more moderate because of the absence of this strong seasonality of litterfall in these forests. If the δ13CR-soil seasonality observed in the present study is broadly representative of this vegetation type, the seasonality might exert a considerable influence on the 13C budget in high-latitude zones because this vegetation type dominates extensive areas of northeastern Eurasia.
4. Summary and Conclusions
 The results of this study indicate that combining high-precision measurements of [CO2] and δ13C with a sampling protocol that minimizes the physical disturbance of the soil permits the precise determination of δ13C of soil-respired CO2 using chamber-based measurements with limited spatial and temporal scales (∼1 m2 and several minutes). However, representation errors (sampling bias) due to spatial heterogeneity in the δ13C of soil-respired CO2 made it difficult to apply the measured values to an analysis of larger spatial scales. Under the current limitations imposed by chamber-based sampling and IRMS-based measurements, we cannot offer a feasible solution that would reduce the representation error to the required level for validating modeled isotopic disequilibrium.
 Even though the chamber-based measurements involve this representation error, the fixed-point regular observations were nonetheless sufficiently useful that we were able to capture the seasonal variation in the δ13C of soil-respired CO2. During our 3-year observation of a deciduous needle-leaf forest, we found significant seasonal variation in the δ13C of soil-respired CO2 even with the influence of root respiration excluded. The δ13C values decreased during the high-temperature season compared with its values during the low-temperature season. In each year, the amplitude of the seasonal change in δ13C exceeded 1‰ and was remarkably larger than the prediction of previous models. In contrast to the soil CO2 efflux, which exhibited a simple exponentially increasing temperature dependence, δ13C showed a characteristic seasonal course in the diagram of δ13C versus temperature. A simple simulation using a two-compartment model illustrated that the characteristic seasonal course of δ13C could be qualitatively explained by accounting for the interplay of three factors: a large difference in δ13C between the labile and resistant compartments of soil carbon, a significant seasonal change in the size of the labile carbon pool, and a higher temperature dependence of the decomposition rate in the labile compartment. The notable seasonality observed in δ13C was probably associated with the characteristic litterfall pattern of this vegetation type.
temporally varying carbon content of soil carbon pool i in the two-compartment model at time t.
atmospheric CH4 mixing ratio.
atmospheric CO mixing ratio.
atmospheric CO2 mixing ratio.
carbon stable isotope ratio (‰).
δ13C of ecosystem-respired CO2 (‰).
δ13C of soil-respired CO2 (‰).
δ13C value for Rh.
δ13C of CO2 from soil heterotrophic respiration (‰).
δ13C of the carbon in compartment i and the CO2 that originates from that comportment.
stem diameter at breast height (cm).
ratio of the carbon decomposed during a 12-month period to the initial carbon abundance in compartment B after the initial input of leaf litter.
Day of year.
photosynthetic isotope discrimination against 13CO2.
respiratory CO2 flux from the terrestrial ecosystem to the atmosphere.
CO2 flux from the atmosphere to the terrestrial ecosystem; counter-flux of Fba.
the compartment number in the two-compartment model.
atmospheric H2 mixing ratio.
decomposition rate constant for carbon pool i in the two-compartment model.
leaf area index (m2).
atmospheric N2O mixing ratio.
change in decomposition rate per 10°C change in temperature.
Rref(i, t) = k(i)C(i, t); Rref
represents the respiration rate at reference temperature Tref.
respiratory flux from component i in month t.
atmospheric SF6 mixing ratio.
soil temperature at time t.
reference soil temperature for which Q10 is calculated.
 We thank our colleagues at the Tomakomai Flux Research Site for their cooperation in this research. We also thank the members of the National Institute for Environmental Studies, who provided useful discussion, many suggestions, and their encouragement in this study. This research was partly funded by the Global Environmental Research Fund, Ministry of Environment, Japan. Finally we earnestly thank anonymous reviewer for helpful and constructive comment on this study.