Use of the isotope flux ratio approach to investigate the C 18 O 16 O and 13 CO 2 exchange near the floor of a temperate deciduous forest

Introduction Conclusions References


Introduction
Stable isotopes of CO 2 have been used to investigate the exchange of carbon dioxide between land and atmosphere (Keeling, 1958;Farquhar et al., 1993;Ciais et al., 1995;Yakir and Wang, 1996;Cuntz et al., 2003).Naturally occurring CO 2 isotopologues, such as 13 CO 2 and C 18 OO, have been used to study the uptake of CO 2 by oceans and land (Tans et al., 1993;Ciais et al., 1995), to investigate the exchange of CO 2 between ecosystems and atmosphere and for partitioning the net CO 2 ecosystem exchange into photosynthetic and respiratory fluxes (Yakir and Wang, 1996;Bowling et al., 2001;Ogée et al., 2004;Zhang et al., 2006).
Published by Copernicus Publications on behalf of the European Geosciences Union.

E. Santos et al.: Use of the isotope flux ratio approach
The isotopologue 13 CO 2 has been used as a tracer in ecosystems where there is a contrast between the isotope compositions (δ 13 C) of growing plants and soil organic matter (Rochette et al., 1999;Griffis et al., 2005b).This contrast is commonly observed either when C 3 plants are growing in soil with organic carbon derived from C 4 residue or vice versa, and it is caused by differences in the photosynthetic isotopic discrimination between C 3 and C 4 plants (Farquhar et al., 1989).On the other hand, the use of C 18 OO as a tracer relies on differences in 18 O composition (δ 18 O) of CO 2 fluxes originating from soil and plant canopies (Gillon and Yakir, 2001).The δ 18 O of canopy and soil CO 2 fluxes is coupled with δ 18 O of soil and leaf water.Differences in δ 18 O between soil and foliage water pools arise as H 16  2 O evaporates more readily than H 18  2 O and due to different evaporation rates between water pools (Farquhar and Cernusak, 2005;Welp et al., 2008).Ogée et al. (2004) proposed the use of carbon and oxygen isotope tracers for partitioning the net CO 2 ecosystem exchange into plant and soil components.The use of C 18 OO is particularly advantageous in established ecosystems where the δ 13 C differences between plants and soil organic matter are not very large (Ogée et al., 2004;Griffis et al., 2005a).
One of main challenges of using C 18 OO as a tracer in ecosystems is its large temporal dynamics (Griffis et al., 2005a;Wingate et al., 2010;Xiao et al., 2010), which is controlled by variables such as changes in environmental conditions, efficiency of the CO 2 hydration, kinetic fractionation, isotopic composition of water in the soil and foliage (Yakir and Sternberg, 2000;Seibt et al., 2006).Seibt et al.(2006) observed that the rate of equilibration between CO 2 and water in soils could not be explained strictly by soil physical properties and hypothesized that the rate of CO 2 hydration was enhanced by the activity of carbonic anhydrase enzyme (CA) in the soil.Soil chamber studies have shown that the effect of CA varies in time and between sites, so additional studies are required to quantify the level of activity of the CA in the soil in different biomes (Seibt et al., 2006;Wingate et al., 2008Wingate et al., , 2010)).Furthermore, chamber studies have brought new insights into mechanisms controlling the C 18 O 16 O exchange in soils; however, the use of soil chambers in ecosystem-scale studies requires a very intensive sampling scheme to characterize the spatial heterogeneity of ecosystem fluxes (Law et al., 1999;Davidson et al., 2002;Powers et al., 2010).In addition, soil chambers can significantly affect the C 18 OO exchange between soil and air, requiring the use of soil diffusion models to correct for this effect (Seibt et al., 2006).
The advent of new measuring techniques, such as quantum cascade laser-based spectrometry (Tuzson et al., 2008;Kammer et al., 2011) and tunable diode laser absorption spectroscopy (Bowling et al., 2003b;Griffis et al., 2005aGriffis et al., , 2008;;Wingate et al., 2010), has allowed near-continuous measurements of CO 2 isotopologues in the air.These measurements can be combined with existing micrometeorological tech-niques, allowing the investigation of isotope exchange in spatial and temporal scales suitable for studying ecosystem biophysical processes (Griffis et al., 2007;2010).Griffis et al. (2004) proposed the use of the isotope flux ratio method (IFR), based on gradient-diffusion theory, to determine the isotope composition of ecosystem respiration.This approach shows some advantages over the commonly used Keeling plot technique (KP) (Keeling, 1958), since it is theoretically less sensitive to changes in background atmospheric CO 2 mixing ratios and provides estimates of flux components that are consistent with the flux footprint (Griffis et al., 2004(Griffis et al., , 2007)).The IFR method could be particularly helpful to study C 18 OO exchange since the conventional KP technique, with concentration data collected during large time intervals (several hours), is not as reliable for determining the 18 O composition of fluxes as when applied to 13 C measurements (Tans, 1998;Flanagan et al., 1999;Griffis et al., 2005a).The IFR method has been applied to investigate the isotope exchange above plant canopies.Studies have shown that the gradientdiffusion theory, in principle, is not suitable to study mass and energy exchange within plant canopies, due to the close proximity of sources/sinks and to the length scale of turbulent eddies inside plant canopies (Corrsin, 1974;Denmead and Bradley, 1987).However, it has been shown that the gradient-diffusion based approaches provide reasonable estimates of fluxes in the open trunk space of forests (Dolman and Wallace, 1991;Baldocchi and Meyers, 1991;Wu et al., 2001).According to the localized near-field theory of Raupach (1989a), a gas constituent that originates from sources at the ground below a vegetation stand can be described by the gradient-diffusion model.
The use of the IFR method beneath plant canopies could bring new insights into mechanisms regulating the isotope exchange in ecosystems.In this study, near-continuous measurements of 12 C 16 O 2 , 13 CO 2 and C 18 OO, obtained using tunable diode laser absorption spectroscopy, were used for the first time with the IFR approach to study the isotopic exchange near the floor of a temperate deciduous forest.Thus, the objectives of this study were 1. to evaluate the use of the IFR method near the forest floor of a temperate deciduous forest by comparing its estimates of isotope composition of CO 2 flux with values provided by a modified KP technique (mKP) and the analytical Lagrangian dispersion analysis proposed by Warland and Thurtell (2000).The latter analysis takes into consideration the proximity of source and sinks and the length scale of turbulence within plant canopies.
2. to compare the δ 18 O of CO 2 flux measured using the IFR near the forest floor with modeled δ 18 O of soil CO 2 flux obtained using an analytical model (Tans, 1998;Amundson et al., 1998;Wingate et al., 2009).This model has been tested in chamber-based studies and can be used to investigate the effect of environmental variables, such as the isotope composition of precipitation and the activity of soil CA on the temporal dynamics of δ 18 O of CO 2 flux near the forest floor (Wingate et al., 2010).

Site description
The experiment was carried out in a deciduous forest at the Environment Canada research station at Borden, ON, Canada (44 The approximately 100-year-old forest, consisting of natural re-growth on abandoned farmland, is composed of mixed hardwood and coniferous species (Neumann and den Hartog, 1989).A survey conducted in 2006 indicates that red maple (Acer rubrum L.) is the predominant tree species (52.2 %) followed by eastern white pine (Pinus strobus L.) with 13.5 %, and large-tooth aspen (Populus grandidentata Michx.) and white ash (Fraxinus americana L.) (∼7 % each) (Teklemariam et al., 2009).In July 2009, the stand height was approximately 22 m and the leaf area index (±SE) was 3.9 (±0.13) m 2 m −2 .The terrain at the site presents variations of elevation within 2 m, except for a 20-m deep and 40-m wide river valley located 1 km south from the 44 m sampling tower and a 6-km wide swamp located 5 km northeast from the tower (Lee et al., 1999).Textural analysis of soil cores indicated loamy sand soil at the site and an increase in the proportion of sand in the soil with depth (Table 1).The averaged carbon content was equal to 2.4 % by mass in the 0-10 cm layer.

Measurements of mixing ratios of stable isotopes of carbon dioxide
Mixing ratios of the isotopologues, 12 C 16 O 2 , 13 CO 2 and C 18 OO, were measured at 10 Hz within the forest canopy and above the forest using a sampling system connected to a tunable diode laser trace gas analyzer (TGA100A, Campbell Scientific, Logan, UT, USA; hereafter TGA), kept in a temperature-controlled enclosure set up in a trailer.The TGA measures the mixing ratio of trace gases in the air by comparing the infrared absorption of sample and reference gas in a specific absorption line of the spectrum.Additional details about stable isotope measurements using the TGA can be found elsewhere (Bowling et al., 2003b;Lee et al., 2005;Griffis et al., 2005a).The air was sampled using eight air intakes, set up within and above the forest canopy at 0.45, 1. 45, 5.51, 9.65, 16.69, 20.77, 25.81 and 36.81 m (Fig. 1).In the first stage of the experiment (day of year, DOY = 182 to 229), only the two closest intakes to the forest floor were sampled during weekends.On week days (Monday to Friday) measurements were taken above the forest; results related to these measurements will be presented in a future study.From DOY 237 to 260, all eight air intakes were sampled.Each air intake consisted of a 1 m stainless tube (0.43 cm I.D.) with a rain diverter and mesh screen in one of its extremities.The other extremity of the tube was connected to a stainless filter (SS-4F-K4-7, 7 µm sintered element filter, Swagelok, OH, USA).In order to prevent condensation, the filter holder was heated using a 0.5 W heater connected to a 12 V DC power supply and a critical flow orifice located downstream of the filter was used to reduce the air pressure in the intake line.Approximately 40 m of polyethylene/aluminum tube (0.43 I.D., Synflex 1300, Aurora, OH, USA) directed the sample to a custom-made manifold (Campbell Scientific).
The manifold was used to control the flow of ambient air from the air inlets and calibration gases through the TGA.The duration of each sampling cycle was 5 min, in which the system measured atmospheric and secondary calibration tank mixing ratios for each isotopologue.The sampling system manifold switched between air intakes every 15 s for 4 min, and then each of the two calibration tanks was sampled for 30 s.The air was pulled continuously through all air intakes at a flow rate of approximately 600 cm 3 min −1 using a vacuum pump (RB0040, Bush Vac.Tec., Boisbriand, QC, Canada).A sub-sample of the total flow was directed to the TGA at a flow rate of 200 cm 3 min −1 in order to maintain the TGA sample cell at approximately 1.8 kPa reducing the pressure broadening of the absorption line (Bowling et al., 2003b).
The secondary calibration tanks were compared weekly with two primary calibration standards obtained from the Stable Isotope Laboratory (SIL) at the Institute of Arctic and Alpine Research, University of Colorado, in cooperation with the Earth System Research Laboratory (ESRL/GMD) of the National Oceanic and Atmospheric Administration.The calibration values for primary standard A were CO 2 mixing ratio = 360.62µmol mol −1 , δ 13 C = −8.475‰ (±0.003 ‰) and δ 18 O = −1.037‰ (±0.006 ‰).Primary standard B consisted of CO 2 mixing ratio = 545.77µmol mol −1 , δ 13 C = −16.202‰ (±0.002 ‰) and δ 18 O = −11.861‰ (±0.007 ‰).The calibration of the secondary tanks followed the two point calibration procedure suggested by Bowling et al. (2003b).An example of corrected mixing ratios for secondary tanks and standard deviations, obtained during a weekly calibration, is shown in Table 2.
TGA measurements during tank calibration were also used to determine the time necessary to flush the TGA sampling cell after switching intakes (Fig. 2).The time required for the TGA to reach 95 % of the total response after switching between high (∼545 µmol mol −1 ) and low (∼330 µmol mol −1 ) 12 C 16 O 2 concentration tanks was ∼4.5 s, which was the same time response obtained for C 18 OO and 13 CO 2 .Thus, the mixing ratios of the two isotopologues for each intake and calibration tanks were extracted from the dataset, discarding 5 s after switching intakes.A total of 50 data points were discarded after switching intakes giving a total of 4800 data points per sampled height and 3000 data points per calibration cycle every 30 min when the TGA system was sampling the two intakes near the forest floor.High-frequency sampling (10 Hz) allows for large number of measurements at each observation height and has the advantage of improving the precision of concentration difference measurements (Wagner-Riddle et al., 2005).The data were averaged into 5 min intervals and corrected using the measurements obtained from each calibration tank during each measuring cycle.The corrected data were used to calculate half-hour mean mixing ratios for each isotopologue.The isotope ratios of CO 2 in the air (δ 13 C a and δ 18 O a ) were expressed according to the delta notation, in reference to the Viena Peedee Belemnite (VPDB) scale, i.e. [ 13 C]/[ 12 C] = 0.0111797, which differs from the Chicago Peedee Belemnite ([ 13 C]/[ 12 C] = 0.112372) by approximately 5 ‰, and [ 18 O]/[ 16 O] = 0.002088349077 (Allison et al., 1995;Griffis et al., 2004).

Supporting measurements
The temporal variation of half-hourly soil CO 2 flux was measured using one automated dark chamber (Li-8100, LI-COR) with a 20 cm diameter.Automated chamber measurements (F static ) were taken every 15 min and averaged into half-hour intervals.To correct F static for the effect of spatial heterogeneity of the soil flux, the net soil CO 2 flux (F R ) was measured weekly using a static chamber at 10 different points in an area adjacent to where the automated measurements were taken.A linear model (F R = 0.727 + 0.623F static , R 2 = 0.88, p < 0.001) was used to scale up the single-point soil chamber measurements, following Ohkubo et al. (2007).Measurements of F R were used for modeling the δ 18 O of net soil CO 2 flux (see Sect. 2.5).
Soil samples were taken weekly to determine the δ 18 O of soil water (δ 18 O sw ) at 5, 10 and 50 cm depth.Liquid water from soil samples was extracted using the cryogenic vacuum extraction method (Ehleringer and Osmond, 1989).In  addition, the δ 18 O of precipitation water (δ 18 O pw ) was determined on an event basis.The precipitation water was collected using a plastic funnel (∼15 cm diameter) placed on the top of a thermally insulated plastic bottle and then stored in sealed glass vials.The δ 18 O of soil and precipitation was determined using the CO 2 equilibration method on a gas bench auto sampler attached to a mass spectrometer (Delta Plus XL, Thermo Finnigan, Bremen, Germany) with precision of 0.1 ‰.Soil temperature (T s ) and water content (θ w ) were measured at 10 cm depth using thermocouples (105T, Campbell Scientific, Logan, UT, USA.) and moisture probes (CS615-L, Campbell Scientific, Logan, UT, USA), respectively.
The precipitation and air temperature were measured in an open pond area adjacent to the site using a tipping bucket rain gauge (Belfort, Baltimore, MD) and air temperature probe (HMP45A, Vaisala, Vantaa, Finland).The wind velocity components were measured at 33.4 m using a sonic anemometer (CSAT3, Campbell Scientific, Logan, UT, USA, Fig. 1).

Determining the δ 18 O and δ 13 C of CO 2 flux near the forest floor
Three methods were used to determine the isotope composition of CO 2 flux near the forest floor: IFR, mKP and WT analysis.Griffis et al. (2004) proposed the gradient diffusion theory to calculate the ratio between fluxes of heavier and lighter isotopologues (F heavy /F light ): where K is the eddy diffusivity, which was assumed to be the same for the heavy and light isotopologues, ρ a is the mean density of dry air, M a is the molar mass of dry air and d[heavy]/dz and d[light]/dz are the time-averaged vertical gradients of the heavy and light isotopologues measured simultaneously at the same height.For practical applications Eq. ( 1a) can be rewritten as where [heavy] and [light] are the half-hour mean mixing ratios of isotopologues, measured at two heights (z 1 = 0.45 and z 2 = 1.45 m) near the forest floor.Large uncertainties in the estimates provided by the IFR method were observed when the gradient of 13 CO 2 mixing ratio was smaller than 0.035 µmol mol −1 m −1 , which, considering the typical proportion of 13 CO 2 in the air, corresponds to a gradient of CO 2 mixing ratio of approximately 3.2 µmol mol −1 m −1 .The same threshold was also observed by Griffis et al. (2005b).Hence, only half-hours, in which the difference of CO 2 mixing ratio between two measurement heights was larger than 5 µmol mol −1 , were used to calculate F heavy /F light , which was expressed in delta notation: The isotope composition of CO 2 flux (δ 18 O F and δ 13 C F ) provided by the IFR approach was compared to δ 18 O F and δ 13 C F estimates derived using a mKP technique.Pataki et al. (2003) recommended the use of a minimum CO 2 mixing ratio range of 75 µmol mol −1 to minimize the errors of the conventional KP approach used with 13 C flask sampling data spanning long periods (hours).However, one of the main limitations of applying KP technique to 18 O is the high variability of δ 18 O of source water in leaves and soil at short time scales (i.e.hours) (Bowling et al., 2003a;Ogée et al., 2004;Griffis et al., 2005a).In this study we attempted to minimize this problem by applying the KP method to derive δ 18 O F for half-hourly periods using 5 min values of CO 2 mixing ratios, δ 18 O a and δ 13 C a measured at 1.45 m above the forest floor (mKP).During half-hour periods, the threshold of mixing ratio (75 µmol mol −1 ) for conventional flask-based Keeling plot is unlikely to be met, so in this study the half-hour Keeling plot data were screened based on the range of mixing ratio (>25 µmol mol −1 ) and R 2 values (>0.95).In addition, the type I regression was used to estimate the Keeling-plot intercept since some bias can be introduced with the type II (geometric) regression when the range of CO 2 mixing ratio is small (Zobitz et al., 2006).In this study we adopted the term mKP to designate the modified Keeling plot approach to emphasize that the period and range of CO 2 mixing ratio were different than what is usually used in the literature.
Estimates of δ 18 O F and δ 13 C F provided by the IFR method were also compared to the Lagrangian dispersion analysis proposed by Warland and Thurtell (2000) (hereafter, WT analysis).The WT analysis was used to infer half-hourly 12 C 16 O 2 . 13CO 2 and C 18 OO fluxes near the forest floor.This formulation is based on Taylor's Lagrangian dispersion theory (Taylor, 1921) and assumes that the canopy is formed by several vertical source layers, each one with a specific value of source strength (S).Over time, each source layer releases a certain amount of matter or energy that is assumed to disperse in a Gaussian fashion.The vertical gradient of concentration (dC/dz) can then be obtained by adding the contributions from each source layer: where i and j are the concentration (C) and source (S) layer indices, respectively, m is the number of source layers, z j is the thickness of the source layer j with respect to the vertical coordinate (z) and M is the dispersion matrix, calculated using profiles of vertical wind velocity (σ w ) and Lagrangian time scale (T L ).Equation ( 3) can be also used to solve the inverse problem (i.e. S from C).Further details on WT analysis calculations are shown in Appendix A.
The flux (F j ) for each source layer is given by Estimated 12 C 16 O 2 , 13 CO 2 and C 18 OO fluxes for the ground level source layer (S 1 ) were converted to delta notation using Eq. ( 3) and compared with the IFR estimates.To do that, z 1 was set to 1.4 m to match the two lowest concentration intake heights.

Modeling δ 18 O F
The δ 18 O of CO 2 flux obtained near the forest floor using the IFR approach was compared with estimates of δ 18 O of net soil CO 2 flux (δ 18 O R ) obtained using an analytical model (Tans, 1998;Wingate et al., 2009).This formulation assumes isothermal and uniform soil water conditions to estimate δ 18 O R : where δ 18 O eq,s (‰, VPDB) is the δ 18 O of CO 2 in isotopic equilibrium with the soil water, ε d,eff is the effective isotopic fractionation during CO 2 diffusion in soil pores, C a is the CO 2 molar concentration (µmol m −3 ) obtained at 0.45 m above the forest floor and F R is the soil CO 2 flux (µmol m −2 s −1 ) measured using soil chambers (Sect.2.3), v inv (m s −1 ) represents the rate at which CO 2 in a column of air exchanges its oxygen atoms with liquid water in the soil (Tans, 1998), which is given by where B is the Bunsen solubility coefficient for CO 2 (Weiss, 1974, B = 1.739 × exp(−0.0390× T s + 0.000236 × T 2 s ), θ w is the soil water content (m 3 m −3 ), D 18 is the effective diffusivity of C 18 OO in soil air, k s is effective rate of oxygen isotope exchange between CO 2 and liquid water (s −1 ): where f CA is the relative increase in hydration resulting from the CA in the soil (Riley et al., 2003;Seibt et al., 2006;Wingate et al., 2008) and k h is the rate of oxygen isotope exchange between CO 2 and water, equal to 1/3 × 0.037 × exp [0.118 × (T s−25)] (Skirrow, 1975;Wingate et al., 2008).Additional details on calculations of parameters used to model δ 18 O R are shown in Appendix B.
3 Results and discussion

Environmental conditions and temporal dynamics of CO 2 isotopes in the air near the forest floor
Rainfall was well-distributed throughout the experiment with the largest daily totals occurring at the end of July (DOY = 207) and beginning of August (DOY 221) (Fig. 4a).
The total precipitation from July to September was 190 mm, which was above the long-term average (144 mm) from 1989 to 2006 for a nearby weather station (Egbert, Environment Canada, 2009).The daily average air temperature during the experiment was slightly cooler (17.5 • C) than the long-term average (17.8 • C).Air temperature reached its maximum in August (DOY 229) and then presented a downward trend until the end of the period (Fig. 4a).Average soil temperature at 10 cm was equal to 22 • C over the study period.Large precipitation events and good drainage favoured by sandy soil at the site (Table 1) contributed to the occurrence of significant variability in the soil water content throughout the season, with soil water content ranging from 0.08 to 0.18 m 3 m −3 at 10 cm depth (Fig. 4b).The half-hourly soil CO 2 flux (F R ) showed similar temporal variation as the soil water content.Higher values of F R (∼6.5 µmol m −2 s −1 , DOY 205) were observed when soil water content values were high, while smaller magnitudes of soil respiration (3.1 µmol m −2 s −1 , DOY 220) were observed during dry periods (Fig. 4c).The ensemble-averaged CO 2 mixing ratio (86 days), δ 18 O a and δ 13 C a obtained near the forest floor show a distinct diurnal pattern (Fig. 5).The CO 2 mixing ratio reached its minimum (379 µmol mol −1 ) in the early afternoon (13:30 h EST), and its maximum (465 µmol mol −1 ) at 08:30 h EST.Data points during liquid nitrogen refilling time were excluded from this Fig.Conversely, δ 18 O a became less negative reaching its maximum value (−0.39 ‰) in the early afternoon and minimum (−2.63 ‰) in the morning.Values of δ 13 C a showed a similar daily trend as δ 18 O a , with values ranging from −11.01 to −7.94 ‰.The causes of this daily pattern of δ 18 O a and δ 13 C a , the expansion of daytime boundary layer, the entrainment of air enriched in 13 C, and 18 O during the daytime and the buildup of CO 2 depleted in the heavy isotopes originated from the soil during low turbulence conditions in the nighttime (Griffis et al., 2004(Griffis et al., , 2005a;;Seibt et al., 2006).

Comparison between isotope flux ratio and Keeling plot approaches
The comparison between δ 18 O F and δ 13 C F estimated using the mKP and IFR methods is shown in Fig. 6.The averages of mKP standard error of intercept were equal to 0.9 ‰ and 1.3 ‰ for δ 18 O F and δ 13 C F , respectively.Only 17 % (δ 18 O F ) and 24 % (δ 13 C F ) of the half-hours analyzed met the criteria used to screen the mKP estimates (CO 2 range >25 µmol mol −1 and R 2 > 0.95).The intercept error was much larger (3.4 and 3.7 ‰, for δ 18 O F and δ 13 C F , respec- tively) when R 2 was not used to screen mKP data.Conversely, 95 % of the half-hour intervals met the criterion used to screen the IFR data obtained close to the forest floor, i.e. difference of CO 2 mixing ratio between the two air intakes near the forest floor was larger than 5 µmol mol −1 .The estimates of δ 18 O F provided by the IFR method showed good correlation (R 2 = 0.80) and agreement (slope = 1.03) with estimates of δ 18 O F obtained using the mKP technique.The regression analysis coefficients were not significant for δ 13 C F (P < 0.01).This can be explained by the relatively large uncertainties in mKP and IFR estimates in comparison to the small range of δ 13 C F values observed for this ecosystem.
The mean (±SE) mKP and IFR δ 13 C F values were −27.5 ‰ (±0.2) and −27.3 ‰ (±0.1), respectively, both within the range of values reported for soil respiration of C 3 ecosystems (Buchmann et al., 1997;Bowling et al., 2005), which provides evidence supporting the validity of these methods inside the forest.Student's t-test showed that the two estimates for δ 13 C F were not different statistically (P > 0.05).
The KP approach has been widely used to determine the 13 CO 2 composition of ecosystem respiration (Pataki et al., 2003).However, previous studies have shown that this approach may not be reliable for inferring the δ 18 O of CO 2 flux (Flanagan et al., 1997;Ogée et al., 2004;Griffis et al., 2005a).Tans (1998) demonstrated that the use of KP approach to estimate δ 18 O R could lead to significant error due the 18 O exchange between CO 2 in the air and soil water, which is also known as abiotic flux or non-respiratory invasion flux (F inv ) (Miller et al., 1999;Riley, 2005), defined as the product of v inv (Eq.6) and C a .Tans (1998) showed that the magnitude of the error in the derived δ 18 O R using the KP approach is proportional to F inv /F R .His simulations indicate that an error of 3 ‰ could occur in δ 18 O F , derived using the KP approach, when F inv /F R is 0.5 and an error of 9 ‰ would be expected for F inv /F R = 2.In this the ratio between modeled F inv and measuredF R was calculated for half-hour periods (shown in Fig. 6), in which δ 18 O F was compared with the mKP approach.The average F inv /F R for these periods was 0.13, and the maximum value for this ratio was 0.19, considering f CA = 1.The good agreement between the IFR and mKP δ 18 O F estimates is encouraging, but  we acknowledge that the magnitude of F inv could be larger due to the activity of the enzyme carbonic anhydrase in the soil (Eqs.7 and 8).The effect of this enzyme on the CO 2 hydration in the soil is not fully understood and shows large temporal and spatial variation (Seibt et al., 2006;Wingate et al., 2008Wingate et al., , 2010)).

Isotope flux ratio and WT analysis comparisons
Estimates of δ 18 O F and δ 13 C F obtained using the IFR were compared with δ 18 O F and δ 13 C F obtained using the WT analysis (Fig. 7).This comparison was only performed for a 23-day period (DOY 237 to 260), when the eight air intakes were sampled continuously within and above the forest canopy.The regression analysis coefficients were not significant (P > 0.05) for the relationships between δ 18 O F and δ 13 C F obtained using IFR and mKP methods.Santos et al. (2011) observed that the WT analysis yielded spurious estimates of CO 2 flux for the lowest source layer in a corn canopy.They hypothesize that the poor performance of the WT analysis was observed when the flows above and within the canopy were decoupled due to poor mixing within the corn canopy.In this study the regression analysis coefficients for the relationship between WT analysis and IFR δ 18 O F were significant (y = −9.9+ 0.28x, R 2 = 0.37, P < 0.01) when only half-hour periods with friction velocity (u * ) ≥ 0.6 m s −1 were included.The mean difference between δ 13 C F estimated by mKP and IFR methods was not statistically significant based on Student's t-test (P > 0.05), as observed previously for the comparisons between mKP and IFR methods.The WT analysis could be used to study isotope exchange within plant canopies; however, additional evaluation of this methodology under different turbulence conditions is still required and needs to be performed in future studies.
A concern that is generally raised when using gradientdiffusion based methods is the occurrence of countergradient fluxes within canopies.Corrsin (1974) observed that a description of the turbulent exchange of scalars using the gradient-diffusion theory is only feasible if the length scale of turbulence is much smaller than the distance over which the gradient of concentration of the transported scalar changes.Wilson (1989) demonstrated that near elevated sources, such as plant canopies, there are substantial changes in gradients of concentration of transported entities over distances much smaller than the length scale of turbulence, expressed by σ w T L , leading to counter-gradient fluxes in some situations.Raupach (1987) used a Lagrangian homogeneous turbulence formulation to demonstrate how counter-gradient fluxes arise in plant canopies.His results showed that counter-gradient fluxes are expected to occur when the transported entity source profile strength shows an intense and localized peak in the foliage well above the ground; however, his simulations do not indicate the occurrence of counter-gradient fluxes in the trunk space near the ground.Wilson (1989) observed that the magnitudes of σ w and T L are small in relation to the gradient of concentration near the surface (Fig. A1), so the gradient-diffusion theory is suitable to investigate the transport of scalars near ground-level sources.Furthermore, previous studies have confirmed the suitability of gradientdiffusion based methods to study scalar exchange in the open trunk space of forests (Dolman and Wallace, 1991;Baldocchi and Meyers, 1991;Wu et al., 2001).These studies and the results obtained here indicate that the IFR is suitable to investigate the isotope exchange in the trunk space near the forest floor.

Comparison between isotope flux ratio estimates and modeled δ 18 O R
The δ 18 O F estimated by the IFR approach near the forest floor was compared with modeled δ 18 O R (Eq. 5) to investigate the impact of environmental variables on the temporal dynamics of δ 18 O F during four selected periods (Fig. 8).These periods were selected because all the measurements required for modeling δ 18 O R were available and the sampling system was being used exclusively to measure the air intakes near the forest floor, resulting in a larger number of data points for each intake and consequently improving the ability of the TGA to measure concentration differences between air intakes (Wagner-Riddle et al., 2005).
Values of F R during the four selected periods ranged from 3.2 (DOY 220) to 6.4 µmol mol −1 (DOY 206) and showed good correlation with the soil temperature (data not shown).Soil water content showed large variation between selected periods as a result of precipitation events and the good soil drainage at the site.During a dry period (DOY 199 to 201), values of θ w showed small variations and average of 10 %; on the other hand for a rainy period (DOY 206 to 208), θ w was higher reaching 23 % after a precipitation event (DOY 206).Average δ 18 O a was −2.9 ‰; however, more depleted δ 18 O a values (−6.3 ‰) were observed after a precipitation event on DOY 207.δ 18 O sw sampled at 10 cm did not show large variations between sampling dates, and further considerations on the δ 18 O sw impact on model calculations will be discussed below.
Figure 8 show also comparisons between δ 18 O F and modeled δ 18 O R .These comparisons rely on the assumption that the variation in δ 18 O F is mainly caused by δ 18 O R dynamics.This was considered a valid assumption since flux ratio measurements were obtained near the ground and the vegetation in the forest understorey was sparse.Estimated values of δ 18 O F using the IFR method ranged from −31.4 ‰ (DOY 208) to −11.2 ‰ (DOY 221).Large variations in δ 18 O F were observed on DOY 206 to 208, when precipitation events caused a reduction in δ 18 O F of approximately 8 ‰ from nighttime periods of DOY 207 to 208.A diurnal variation in δ 18 O F was observed on DOY 213, 220 and 221, with more depleted δ 18 O F present during daytime.Wingate et al. (2010) also reported more depleted δ 18 O R values in the daytime in a maritime pine stand, which were synchronized with variations in δ 18 O a and F R .In their study δ 18 O a was more enriched during the daytime, similarly to the δ 18 O a daily trend observed in the present study (Fig. 5).On the other hand, Seibt et al. (2006) observed an opposite trend in δ 18 O a close to the soil surface, with values around 3 ‰ during the night-and −2 ‰ in the daytime.They observed that daily variations in δ 18 O R were coupled with δ 18 O a .In this study δ 18 O a and δ 18 O R were not well coupled (Fig. 8) and this could not explain diel changes in δ 18 O R .One hypothesis to explain our daily variations in δ 18 O R is that diel variations in δ 18 O sw could lead to changes in δ 18 O R , but a more frequent soil water sampling scheme would be required to test this hypothesis.
The mean differences between δ 18 O F and modeled δ 18 O R over the whole period were equal to 4.2, 0.53 and 4.8 ‰ for f CA = 1, 20 and 100, respectively (Fig. 8).Wingate et al. (2010) observed that a temporally uniform f CA = 70 improved the agreement between modeled δ 18 O sw and estimated from the oxygen composition of the net CO 2 flux obtained during a 20-day period.Our results show that the use of f CA = 20 could minimize the differences between δ 18 O F and modeled δ 18 O R over the whole period.However, the use of a single value of f CA over the whole period could not explain diel variations in δ 18 O F .The daytime depletion in δ 18 O F (DOY 200,213 and 220), for example, required larger values of f CA to improve the daytime agreement between modeled and measured values when compared to the f CA values used for the nighttime.Seibt et al. (2006) used a multi-layer model to study the temporal dynamics of δ 18 O R in a P. sitchensis plantation.Their results also indicate large temporal variation of f CA , requiring the use of f CA values ranging from 80 to 1000 for soil top layer to match chamber observations during three sampling campaigns.The use of large values of f CA results in shallower z eq (see Appendix B).In this study typical values of z eq were 7, 1.5 and 0.6 cm for f CA = 1, 20 and 100, respectively.We acknowledge that the extrapolation of δ 18 O sw beyond the sampling depths could lead to errors in δ 18 O R estimates, especially when large gradients of δ 18 O sw were observed close to the soil surface (DOY 211, Fig. 3).An arbitrary reduction of 2 ‰ (VSMOW) in δ 18 O sw resulted in a decrease of ∼4 ‰ (VPDB) in δ 18 O R values, assuming f CA = 100.Thus, more superficial soil sampling could be beneficial when using this model for estimating δ 18 O R.
On DOY 220 to 222 δ 18 O F , values showed an upward trend, which was coupled with F R variation; however, this trend was not captured by the δ 18 O R model.Wingate et al. (2008) observed that, besides the effect of the CA, an evaporative enrichment of 3 ‰ in δ 18 O sw values was required to improve the agreement between modeled δ 18 O R and soil chamber observations during a 3-day period in a Mediterranean soil.In this study, an enrichment of ∼2.5 ‰ (VS-MOW) in δ 18 O sw from DOY 220 to 222 (before precipitation event) would be necessary to improve the agreement between modeled δ 18 O R and measured δ 18 O F for a constant f CA = 20.
Large disagreement between modeled δ 18 O R and δ 18 O F was observed after precipitation events, which was likely due to changes in δ 18 O sw .A decrease of approximately 5 ‰ in δ 18 O sw would be required to match measured with modeled δ 18 O R values on the nighttime of DOY 208, assuming a constant f CA = 20.These results show that changes in δ 18 O sw caused by precipitation events are unlikely to be properly represented by the weekly soil water sampling scheme performed in this study.The proper characterization of δ 18 O sw would require more frequent soil sampling or δ 18 O sw modeling approaches that take the δ 18 O of precipitation into consideration (Braud et al., 2005;Wingate et al., 2010).

Conclusions
The IFR and mKP methods showed very good agreement (slope = 1.03) and good correlation (R 2 = 0.80) when used to estimate half-hourly δ 18 O F .The mean (±SE) mKP and IFR δ 13 C F values were −27.5 ‰ (±0.2) and -27.3 ‰ (±0.1), respectively, both within the range of values reported for soil respiration of C 3 ecosystems (Bowling et al., 2005), which provides evidence supporting the validity of these methods inside the forest.The comparisons between IFR and mKP techniques are encouraging, as they show that the IFR method can be used to study the isotope exchange near the forest floor.The large amount of data captured (∼95 % of half-hour periods evaluated) for the IFR method compared to the mKP method provides new opportunities for the study of δ 18 O F dynamics within forest canopies.
The coefficients of the regression analysis between WT analysis and IFR were not significant (P > 0.05).However, better correlation (R 2 = 0.37) between WT analysis and IFR δ 18 O F was obtained when only turbulent periods (u * ≥ 0.6 m s −1 ) were included in the analysis.During low turbulence periods, the decoupling between above and within canopy flows could be one of the reasons for the poor agreement between the two methods.Further investigation on the use of the WT analysis to study the isotope exchange in ecosystems is still necessary.
The δ 18 O of CO 2 flux near the forest floor showed large temporal variation, with values ranging from -31.4 ‰ (DOY 208) to -11.2 ‰ (DOY 221).Precipitation events caused substantial variation (∼8 ‰) in δ 18 O F over a period of approximately 24 h.A diel trend of δ 18 O F was also observed, with more negative values being observed during the daytime.The use of a single value of f CA over the whole period could not explain the diel variation of δ 18 O F .The results also show the importance of a frequent soil sampling scheme for the accuracy of modeled δ 18 O R values.

Appendix A
WT analysis and turbulence statistics calculations Warland and Thurtell (2000) used a dispersion matrix (M) to relate the concentration profile with the source strength distribution of transported scalars within plant canopies (Eq.4).A full description of this analysis and details in the derivation of M can be found in Warland and Thurtell (2000).The dispersion matrix M is calculated using turbulence statistics at source and concentration measurement heights: where L L is the Lagrangian length scale, given by L L = σ w T L , z i and z j are the heights of the concentration measurements i and of the source layer j , respectively, and G ij represents the image source, specified to create a reflecting boundary (Warland and Thurtell, 2000): The parameterizations of turbulence statistics proposed by Leuning et al. (2000) and Styles et al. (2002) were used to estimate σ w and T L profiles, respectively (Fig. A1).Leuning et al. (2000) used exponential and non-rectangular hyperbolic functions to describe the profile of σ w :  where u * is the friction velocity, obtained using sonic anemometer set up at 33.4 m (Sect.2.3), h is the canopy height, c 1 = 0.2, c 2 = 1.5, a = 0.85, b = 0.4, d 1 = −1 and θ = 0.98.The σ w profiles obtained using these equations are in agreement with turbulence measurements, reported by Raupach (1989b) and obtained for seven different canopies (two corn and forest canopies and three wind tunnel models).Styles et al. (2002) proposed the following function to describe the profile of T L within and just above plant canopies: where c 3 and c 4 are fitted coefficients.We adopted values for c 3 (= 4.86) and c 4 (= 0.10), obtained by Haverd et al. (2009), using an optimization procedure to improve the agreement between modeled and measured concentration profiles of temperature, water vapour and CO 2 concentration in a temperate eucalyptus forest.The parameterizations of turbulence statistics described above were developed under neutral atmospheric conditions, so atmospheric stability functions proposed by Leuning (2000) were used to correct the profiles of σ w and T L for non-neutral conditions.Equation (4) needs to be integrated to be used with discrete measurements.This integration was performed using the trapezoidal rule from the concentration measurement height (z i ) to the reference height (z R = 36.81m), reducing the sensitivity of the source to small gradients between adjacent heights when solving the inverse problem (Qiu and M ij + M (i+1)j S j z j z i (A5) where C r and C i are the concentrations at z R and z i , respectively, m (= 4) is the number of source layers, and n (= 8) is and the number of concentration measurement heights.The use of redundant concentration data (n > m) reduces source strength uncertainties originating from errors in the concentration or turbulence statistics profiles (Raupach, 1989b).
In the present study, a layer thickness z i = 0.01 m was used in Eq. (A5), following Qiu and Warland (2006).C 16 O 2 and C 18 OO source strengths were inferred within the forest canopy using concentration measurements obtained when the TGA sampling system was set to sample eight air intakes within and above the forest canopy (Sect.2.2).

Appendix B
Calculation of parameters used to model δ 18 O of soil CO 2 flux The isotope composition of CO 2 in isotopic equilibrium with the soil water (Brenninkmeijer et al., 1983), used in Eq. ( 6), was calculated as follows: δ 18 O eq,s = δ 18 O sw + 17604 (T s + 273.16) − 17.93 (B1) where δ 18 O sw is the isotopic composition of soil water at the equilibration depth (z eq ), z eq = 2 2 ln 2D 18 k s Bθ w , which is defined as the shallowest depth at which full isotopic equilibration between water and CO 2 molecules occurs (Wingate et al., 2009).δ 18 O sw profiles were obtained as described in Sect.2.3 and were converted into the VPDB scale to be used in Eq. (B1).The effective kinetic fractionation (ε d,eff ) was calculated following Wingate et al. (2009): where ε d is the full kinetic fractionation during CO 2 diffusion in soil pores, equal to -8.7 ‰ (Tans, 1998), , and z o is the soil column depth over which uniform CO 2 production occurs, assumed to be equal to 0.15 m in this study (Riley et al., 2003).
The effective diffusivity of C 18 OO in soil air is given by D 18 = D s α d , with α d = 1 + ε d /1000, and D s the diffusivity of CO 2 in soil air (Moldrup et al., 2003): where D 25 is the molecular diffusivity of CO 2 (1.4 × 10 −5 m 2 s −1 ) at 298 K; θ a is the proportion of soil pores filled with air; θ a = θ satθ w , where θ sat is the soil water content at saturation estimated to be 0.46 m 3 m −3 at the site (Saxton and Willey, 2006), b is the soil water retention parameter, determined to be equal to 6.2 in this study (Cosby et al., 1984), T 25 = 298 K and n is 1.5 (Bird et al., 2002).

Fig. 1 .
Fig. 1.Experimental setup used to study C 16 O 2 and C 18 OO exchange in a temperate deciduous forest in Borden, ON, Canada.TGA denotes tunable diode laser; P shows placement of vacuum pumps.Placements of the automatic soil chamber used to measure the soil CO 2 flux and sonic anemometer are also shown.

Fig. 2 .
Fig. 2. Average 12 C 16 O 2 mixing ratios (±1 standard deviation) measured during switching between secondary calibration standards at 10 Hz (n = 44).The solid horizontal lines indicate the times (0 and 30 s) when the TGA sampling system switched from low (327 µmol mol −1 ) to high (∼543 µmol mol −1 ) concentration calibration tanks, and dotted lines indicate the times (4.4 and 4.5 s) after switching air intakes at which TGA readings reached 95 % of the total response.

Fig. 3 .
Fig. 3. Measured (symbols) and fitted (lines) profiles of 18 O values for soil water (δ 18 O sw ) for three sampling dates (day of year, DOY = 198, 211 and 217) in a temperate deciduous forest.Here δ 18 O sw is expressed in the VSMOW scale and was sampled at three depths: 0.05, 0.10 and 0.50 m.Fitted curves are exponential functions with e-foldings of 5 cm (DOY = 198 and 217) and 8 cm (DOY = 211).

Fig. 4 .
Fig. 4. (a) Daily total precipitation (bars) and mean air temperature (solid line), (b) daily mean soil temperature (solid line) and mean soil volumetric water content (θ w , dashed line) at 10 cm depth, (c) half-hourly soil CO 2 flux (F R ).The gaps observed in F R data were caused by automatic soil chamber failure.

Fig. 5 .
Fig. 5. Ensemble half-hourly average of CO 2 mixing ratio and isotopic compositions of CO 2 (δ 18 O a and δ 13 C a , VPDB scale) in the air at 1.45 m above the floor of a deciduous temperate forest from day of the year 188 to 274 in 2009.The error bars indicate ±1 mean standard error.Data from 10:00 to 11:00 h (EST) were discarded due to liquid nitrogen filling time, which resulted in fewer data points than the remaining hours of the day.

Fig. 6 .
Fig.6.Relationship between half-hourly isotopic ratios of the CO 2 flux near the forest floor (δ 18 O F , δ 13 C F ) estimated using Keeling plot (± standard error of intercept) and isotopologue ratio method in the understory of a deciduous forest.

Fig. 7 .
Fig. 7.Relationship between half-hourly isotopic ratios of the CO 2 flux near the forest floor (δ 18 O F and δ 13 C F ) estimated using a Lagrangian dispersion analysis (WT analysis) and flux ratio method in the understory of a deciduous forest.u * is the friction velocity (m s −1 ).

Fig. 8 .
Fig. 8. Half-hour values of soil CO 2 flux (F R ), soil water content (θ w ) and C 18 OO composition of the air (δ 18 Oa, blue solid line), expressed using the VPDB scale, during four selected periods.H 18 2 O composition of the soil water (δ 18 Os, VSMOW scale) at the 10 cm depth between two sampling dates.C 18 OO composition of CO 2 flux (δ 18 O F ) near the forest floor obtained using the isotope flux ratio method (δ 18 O F,IFR , open circles) and modeled δ 18 O of net soil CO 2 flux (lines) according to Wingate et al. (2009) using three values for the relative increase in hydration due to the enzyme carbonic anhydrase activity in the soil (f CA , Eq. 7) in a temperate deciduous forest.The δ 18 O of CO 2 flux is expressed in the VPDB scale.Shaded areas in the graph indicate nighttime periods, and arrows indicate precipitation events with respective isotope composition of precipitation water expressed in the VSMOW scale.

Table 1 .
Textural composition and organic carbon content of the soil in a deciduous forest.* soil texture analysis was obtained from three soil cores.Numbers in brackets are ±1 standard deviation * * soil carbon content from nine soil cores.

Table 2 .
CO 2 isotopologues mixing ratio (± mean standard error) of secondary calibration tanks obtained during weekly calibration on day of year 188.
F is the isotope ratio of the CO 2 flux, reported in parts per thousand (‰) in this study.R F is the ratio between the heavier and lighter isotopologue fluxes (F heavy /F light ) defined as F 13 /F 12 for 13 CO 2 and 12 CO 2 fluxes, or 0.5 F 18 /F 16 for C 18 O 16 O and C 16 O 2 fluxes, and R VPDB is the molar ratio ( 13 C/ 12 C or 18 O/ 16 O) of Viena Peedee Belemnite.