The current emphasis on global climate studies has led the scientific community to set up a number of sites for measuring the long-term biosphere-atmosphere net CO2 exchange (net ecosystem exchange, NEE). Partitioning this flux into its elementary components, net assimilation (FA), and respiration (FR), remains necessary in order to get a better understanding of biosphere functioning and design better surface exchange models. Noting that FR and FA have different isotopic signatures, we evaluate the potential of isotopic 13CO2 measurements in the air (combined with CO2 flux and concentration measurements) to partition NEE into FR and FA on a routine basis. The study is conducted at a temperate coniferous forest where intensive isotopic measurements in air, soil, and biomass were performed in summer 1997. The multilayer soil-vegetation-atmosphere transfer model MuSICA is adapted to compute 13CO2 flux and concentration profiles. Using MuSICA as a “perfect” simulator and taking advantage of the very dense spatiotemporal resolution of the isotopic data set (341 flasks over a 24-hour period) enable us to test each hypothesis and estimate the performance of the method. The partitioning works better in midafternoon when isotopic disequilibrium is strong. With only 15 flasks, i.e., two 13CO2 nighttime profiles (to estimate the isotopic signature of FR) and five daytime measurements (to perform the partitioning) we get mean daily estimates of FR and FA that agree with the model within 15–20%. However, knowledge of the mesophyll conductance seems crucial and may be a limitation to the method.
 Terrestrial ecosystems are a major component of the climate system through the exchange of energy, momentum, and trace gases with the atmosphere. The spatial and temporal variations of these exchanges are difficult to assess because they involve several physical and biological processes acting at different scales. This is true, in particular, for CO2 exchange.
 In the absence of human activity net CO2 exchange between terrestrial ecosystems and the atmosphere (net ecosystem exchange, NEE) is the result of carbon uptake during photosynthesis (gross primary production, GPP) and carbon losses during respiration (total ecosystem respiration, TER). TER is a composite flux, involving respiration by foliage, stem, and roots (autotrophic respiration), and respiration by soil organisms (heterotrophic respiration).
 A range of multiscale research tools is required to improve our understanding of ecosystem functioning [Canadell et al., 2000; Running et al., 1999]. The net CO2 flux is now measured continuously at more than 100 continental sites within the world wide network FluxNet using the eddy-covariance technique [Aubinet et al., 2000; Baldocchi et al., 2001]. Combined with CO2 storage measurements this leads to accurate estimates of NEE at an hourly timescale, at least during daytime periods (see below). However, partitioning NEE into its components GPP and TER remains necessary to understand the spatial and temporal variations in this exchange [Janssens et al., 2001; Valentini et al., 2000]. The difficulty is that NEE is typically an order of magnitude smaller than these two nearly offsetting terms.
 The most straightforward way to estimate TER consists in making leaf, stem, and soil chamber measurements, and scaling them up to the ecosystem level [e.g., Goulden et al., 1996; Granier et al., 2000; Lavigne et al., 1997]. However, this time expensive method requires a heavy experimental setup that cannot be installed routinely at all FluxNet sites. A simple commonly used approach to estimate TER is based on regressions of nocturnal NEE versus soil or air temperature measurements [e.g., Janssens et al., 2001; Valentini et al., 2000]. One difficulty is to get accurate eddy flux measurements during nighttime periods. Indeed, at night, the atmosphere is often stratified and turbulence is sporadic so that other forms of transport, not captured by the eddy-covariance technique (e.g., advection), may become more important. This can lead to an underestimation of TER of up to 30% [Goulden et al., 1996; Lavigne et al., 1997]. In addition, daytime TER is likely to differ from nighttime TER because of light-induced inhibition of leaf respiration [Brooks and Farquhar, 1985; Villar et al., 1995]. Extrapolating the regressions found on nocturnal data to daytime periods can therefore lead to an overestimation of TER of up to 15% [Janssens et al., 2001]. Alternate methods to partition NEE into GPP and TER that can be easily applied at the various FluxNet sites must be found in order to reduce the uncertainties on these two terms.
 Following an idea of Yakir and Wang , Bowling et al.  suggested a method to partition NEE into net assimilation FA (|FA| = |GPP| – daytime foliar respiration) and nonfoliar respiration FR (FR = TER – foliar respiration if daytime) by combining eddy flux measurements and 13CO2/CO2 ratio measurements (hereafter referred to as the EC/flask method). Plants assimilate preferentially the light isotope of CO2 during photosynthesis, leaving the atmosphere enriched in 13C relative to plant biomass. Since there is apparently no fractionation associated with respiration [e.g., Lin and Ehleringer, 1997], the respired CO2 has the isotopic composition of soil and plant biomass (or assimilates) and is therefore depleted in 13C relative to the atmosphere. Thus a diurnal cycle is apparent in the isotopic composition of air CO2 that seems to contain enough additional information to allow the partitioning of NEE into FA and FR. However, a simple model for canopy conductance is needed to estimate the total ecosystem fractionation associated with net photosynthesis. This requirement is responsible to a large extent for the limitations of the method [Bowling et al., 2001].
 The objective of the present paper is to investigate the applicability of this method on a routine basis, i.e., by collecting less isotopic measurements at each campaign, but more regularly during one growing season. To answer this question we first apply the EC/flask method of Bowling et al.  at a coniferous temperate forest site that was subject to intensive isotopic measurements in the air, the soil, and the biomass in summer 1997, and test its ability to estimate FA and FR. We also adapt the multilayer soil-vegetation-atmosphere transfer model MuSICA [Ogée et al., 2003] to compute flux and concentration profiles of 13CO2. Using the model as a “perfect” simulator, and taking advantage of the very dense temporal and spatial resolution of the isotopic data, it is possible to understand how each hypothesis underlying the EC/flask method affects the value of FA and FR. Next, we study the impact of retaining only a subset of the isotopic data on the retrieval of FA and FR, from which we formulate an efficient and cost-effective sampling strategy.
2. Theoretical Background
 In this section we briefly recall the equations used by Bowling et al.  to partition NEE into FA and FR. For clarity the same notations and conventions are used, except for the storage terms for which the notation seemed misleading.
where ρ is the air molar density (mol m−3), Ca (mol mol−1) is the CO2 concentration at height z and time t, F (mol m−2 s−1) and S (mol m−3 s−1) are the CO2 flux and source density (at level z and time t), and zr is a reference height above the vegetation. Equation (1a) can be rewritten as:
where is the net CO2 flux above vegetation (measured by eddy-covariance at level zr, the over bar denoting Reynolds averaging and the primes denoting fluctuations from this average) and ρ〈dCa/dt〉 is the CO2 air storage between the ground and the level above vegetation at which the net CO2 flux is measured. By convention upward scalar fluxes are positive.
 Conservation of mass for 13CO2 is given by:
where ΔA is the fractionation factor associated with net photosynthesis, and Rr and Ra refer to the 13CO2/CO2 ratios in canopy air and respired CO2. Rewriting this equation in δ notation (δ = R/RPDB − 1, where RPDB is the isotope ratio of the Pee Dee Belemnite standard) gives:
where ρ is the so-called eddy isoflux [Bowling et al., 2001] and ρ〈dCaδa/dt〉 is the isostorage, i.e., the 13CO2 air storage in δ units. Equations (1) and (3) can then be rewritten as:
Equations (4a) and (4b) can be seen as a system of two equations with two unknowns (FA and FR). To solve this system in FA and FR we need to know all other variables, i.e., storage, isostorage, eddy flux, eddy isoflux, δr, δa, and ΔA.
 The eddy flux is measured by eddy-covariance at a reference level zr above vegetation. The storage and isostorage terms are computed from air CO2 concentration and 13CO2/CO2 ratio measurements at different heights between the ground and the level where the eddy flux is measured. Bowling et al.  computed the eddy isoflux by expressing δa as a linear combination of Ca during daytime and using this relationship to retrieve a 10-Hz time series for δa:
 They verified empirically that such a linear relationship between δa and Ca holds from a variety of timescales (500 ms, 30 s, and 30 min).
where is the fractionation resulting from the diffusion of CO2 between the canopy air space and the sites of carboxylation, b is the net fractionation of the enzyme-catalyzed fixation of CO2 [≈27‰, Farquhar et al., 1989; Farquhar and Lloyd, 1993], and Cc is the CO2 concentration at the carboxylation sites. Neglecting the resistance for CO2 diffusion from the stomatal cavity to the mesophyll wall with respect to the stomatal resistance leads to [Farquhar et al., 1989; Farquhar and Lloyd, 1993]:
where gc is the bulk canopy conductance for CO2 (the stomatal conductance at the leaf scale, see equation (9) below), ga is the aerodynamic conductance for CO2 diffusion in air, rm is the resistance to CO2 diffusion within the mesophyll, ab is the fractionation associated with diffusion in the laminar boundary layer (2.9‰), a is the fractionation due to molecular diffusion from the leaf surface to the substomatal cavity (4.4‰), as(T) is the fractionation as CO2 enters solution (1.1‰ at 25°C), and al is the fractionation caused by diffusion within the cell (0.7‰). The aerodynamic resistance 1/ga is expressed as the sum of a turbulent resistance 1/gt and a boundary layer resistance 1/gb [Lamaud et al., 1994]. The value of varies between about 3.6‰ (in the morning when gc takes its maximum value) and a = 4.4‰ (during the night when gc = 0).
Equation (7) was obtained by using the standard “big leaf” multiple resistance model. In this framework, Cc is given by:
 The bulk canopy conductance gc is given by the Penmann-Monteith equation:
where s (kg kg−1 K−1) is the slope of the saturation vapor pressure versus temperature curve, Rn, LE, and G (W m−2) are net radiation, latent, and storage heat fluxes, respectively, cp (J kg−1 K−1) is the specific heat of air, Da (kg kg−1) is the air saturation vapor deficit, and γ = cp/L (K−1) is the psychrometric constant. The 1.6 factor arises in the conversion from conductance for CO2 to H2O.
 The conductances g′a and g″a are the counterparts of ga for water vapor and sensible heat, respectively, and are given by:
 The 1.4 and 0.92 factors arise from the conversion of conductances for CO2 to conductances for H2O or sensible heat.
 The expression for gt uses the friction velocity U*, i.e., the square root of the momentum flux at the reference level above vegetation, and the mean wind speed Ur at the same height. This expression is true for stable and near-neutral conditions but in unstable conditions this amounts to neglecting the differences in stability corrections between momentum and scalars. However, this approximation turns out to be much better than trying to evaluate gt from surface layer log law, since our measurement level is well within the roughness sublayer. The expression for gb makes use of the inverse Stanton number (B ≈ 1/7.5, as given by Lamaud et al.  at the same site), the Schmidt number for CO2 (Sc = 1.02) and the turbulent Prandtl number (Pr = 0.72), so that it reduces to gb ≈ U*/10.
 The EC/flask method can be decomposed into several steps (Figure 1). Nighttime air isotopic data are needed to determine δr (see below), while daytime data are used to estimate both the eddy isoflux (equation (5)) and the isostorage. The Penmann-Monteith equation is used to estimate the bulk canopy conductance and ΔA. Finally, from equations (4a) and (4b) we can retrieve FR and FA. The assumptions underlying each of these steps are critically analyzed and tested in what follows.
3. Materials and Methods
3.1. Research Area
 The experimental site is located at about 20 km from Bordeaux, France (44°43′N, 0°46′W, altitude 62 m) in a nearly homogeneous maritime pine stand (Pinus pinaster Ait.) planted in 1970. The trees are distributed in parallel rows along a NE-SW axis with an interrow distance of 4 m. In September 1997 (period at which the isotopic measurements were performed), the stand density was 520 trees per hectare; the mean tree height was about 18 m and the projected leaf area index was around 3. The canopy is confined to the top 6 m [Porté et al., 2000] so that canopy and understorey constitute two separate layers. The latter is mainly made of grass (Molinia coerulea) whose roots and stumps remain throughout the year but whose leaves are green only from April to late November, with maximum leaf area index and height of 1.4–2.0 and 0.6–0.8 m, respectively [Loustau and Cochard, 1991; Ogée et al., 2003]. A 5-cm thick litter made of compacted grass and dead needles is present all yearlong. The water table never goes deeper than about 200 cm. In September 1997, soil water content in the top 80 cm went down to 60 mm so that the effect of water stress on CO2 and water vapor exchanges was noticeable [Ogée et al., 2003].
3.2. Flux and Meteorological Measurements
 The experimental setup that provided the flux and meteorological measurements used here was installed following the requirements of EUROFLUX (the European network in FluxNet). At 25 m above ground, considered here as our reference level zr, the following data were measured every 10 s and averaged every 30 min: net radiation with a Q7 net radiometer (REBS, Seattle, WA); incident solar radiation with a C180 pyranometer (Cimel, France); air temperature and specific humidity with a 50Y temperature-humidity probe (Vaisala, Finland). Wind speed, friction velocity, and sensible heat flux were measured with a 3D sonic anemometer (Solent R2, Gill Instruments, Lymington, Hampshire, UK), and water vapor and carbon dioxide fluxes were computed using the sonic anemometer coupled with an infrared gas analyzer (LI-6262, LICOR, Lincoln, NE, USA). Rainfall was measured at 20 m with an ARG100 rain gauge (Young, USA). All additional details can be found in the work of Berbigier et al. .
3.3. Air CO2 Measurements
 Ambient air samples from 11 heights (0.01, 0.2, 0.7, 1, 2, 6, 10, 14, 18, 25, and 38 m) were pumped continuously during a 2-month period starting on 4 September 1997. The pump was coupled with an electrovalve to scan the various levels every 2–3 min and a second infrared gas analyzer (LI-6262, LICOR, Lincoln, NE) was used (in the absolute mode) for CO2 analysis. Half-hour time series were then computed by linear interpolation. The overall precision of air CO2 measurements was estimated at ±10 ppmv, which includes both measurement and sampling errors.
3.4. Isotope Measurements
 All isotopic measurements were made on 4 September (day 247) and the following night.
 Ambient air samples from the same 11 levels used for CO2 sampling were predried by passage through a mixture of ethanol-solid carbon dioxide to remove H2O and collected every half-hour (night) or every hour (day) into glass flasks for isotopic analysis. A total of 341 flasks were analyzed. The analysis of δ13CO2 was performed using a gas chromatograph (Hewlett Packard 5890 Series II, Hewlett Packard Co. Ltd) coupled with an isotope ratio mass spectrometer (Optima, Fisons Instruments, Valencia, CA).
 Tree collar and foliage (needle and leaf) samples were collected each hour from trees and grass samples near the mast for stable isotope analysis. Tree collar samples were collected by coring the trunks at 0.5 m from ground level with an increment borer. Soil profiles were drilled with an auger at 0.025 m intervals from 0 to 0.05 m below the surface and at 0.05 m intervals from 0.05 to 0.5 m.
 Total organic material was dried in a vacuum line at 60°C. Dried material was crumbled into a fine powder (<100 mm) and carefully homogenized and combusted in an elemental analyzer (CHN-type, NA 1500, Fisons Instruments, Valencia, CA, USA). Evolved gases were cryogenically purified and separated in a trapping system with different and variable temperatures, and finally introduced in a gas isotope ratio mass spectrometer (SIRA 10, Fisons Instruments, Valencia, CA, USA) equipped with double inlet system and triple ionic collection.
 Carbon isotope ratios are calculated as:
where Rsample and RPDB are the 13C/12C ratios of the sample and the Pee Dee Belemnite standard, respectively. The overall precision of the carbon isotope measurements is ±0.3‰.
3.5. MuSICA Model
 The MuSICA model is a multilayer multileaf biophysical soil-vegetation-atmosphere transfer model [Ogée et al., 2003]. Its key features are that (1) in each vegetation layer, the model distinguishes several types of “big leaves” (or “big shoots”) according to their age, sun exposure (sunlit or shaded), and water status (wet or dry) and (2) the transport of the different atmospheric scalars (temperature, water vapor, CO2, …) is described with a Lagrangian turbulent transfer model [Raupach, 1989b], and for different atmospheric stability conditions.
 For this study the total number of layers is set to 36 with 30 layers within the vegetation and 3 layers in the understorey (instead of 12, 10, and 1, respectively, of Ogée et al. ) in order to better capture the shapes of the scalar profiles within the vegetation. We also added the transport of the 13CO2 tracer (see Appendix A). This version of MuSICA is then able to compute air CO2 and δ13CO2 profiles, and the various components of the carbon budget, GPP, TER, but also FA and FR. It is therefore suitable to test the different assumptions underlying the EC/flask method.
4. Results and Discussion
4.1. Meteorological Conditions
 The isotopic measurements were performed during one single 24-hour period. As in the work of Bowling et al. , we used these measurements to estimate the three coefficients δr, m, and p in equations (4) and (5). Then assuming that these coefficients do not change much over time, we applied the EC/flask method to partition NEE into FA and FR on a longer period. On day 269, a strong storm occurred so that we preferred to restrict this analysis to 22 days only. The meteorological variables during this 22-day period (comprising the day of measurements and the following 21 days) are shown in Figure 2. We can see that this period includes mostly sunny days with a few cloudy days (249, 255–257, and 263–265), characterized by colder and moister air. It occurred at the end of summer, at a time when the soil water content had fallen below 70 mm and water stress was noticeable on water vapor flux (see below and Figure 3). Only one light rain event occurred on day 255 but the amount of rainwater did not exceed 7 mm. We must notice that the whole period is characterized by a light wind (less than 3 m s−1), especially during the night and in the early morning. This is usually in favor of rapid changes, from stable to unstable, of the atmospheric conditions which are difficult to model correctly and may compromise the model performance (see below).
4.2. Evaluation of the Model Behavior
Figure 3 shows the measured and modeled turbulent fluxes for sensible heat, water vapor, and CO2 over the 22-day period. Generally, the MuSICA model reproduces correctly the diurnal variations of all fluxes [see also Ogee et al., 2003]. In particular, the effect of cloudiness and water stress on latent heat and CO2 fluxes seems well accounted for. However, at some specific times the modeled fluxes show rapid temporal variations. This is particularly the case for the CO2 flux. These rapid variations mostly occur during the night or in the early morning (i.e., when the wind is low), and result from an excessive CO2 storage term usually followed (the next time step or later) by a flush out of the same order of magnitude.
 In MuSICA, scalar profiles are computed iteratively because they depend on the scalar source densities, which in turn depend on the scalar profiles. In addition, the turbulent transport module in MuSICA requires steady turbulence: at each time step a new profile is computed in “equilibrium” with the scalar source densities and without keeping memory of the scalar profile at the previous time step. When wind velocity is low the model does not always converge properly because it can switch from very stable to very unstable conditions, depending on the sign of the sensible heat flux. In such case, the predicted scalar profile is numerically unstable, and combined with the previous scalar profile, it may result in excessive air storage terms. Note that at night, CO2 concentrations in the understorey are often 150 ppmv larger than at the reference level. A flush out of only 50 ppmv over a 25-m high air column during one time step of 1800 s corresponds to a flux of more than 25 μmol m−2 s−1, which is an order of magnitude larger than the nighttime CO2 flux. This explains why MuSICA can easily predict rapid CO2 flux variations with wrong but still realistic values of air CO2 concentrations.
Figures 4a and 4b show the measured and modeled air CO2 and δ13CO2 profiles at different times of day 247. It can be seen that the model correctly reproduces the different profiles, but systematically underestimates the CO2 and 13CO2 nighttime gradients above the understorey (between 1 and 6 m). We also notice that the disagreement between model and measurements has always the same tendency for both CO2 and δ13CO2 profiles, which indicates a consistency between the two tracers, and between model and measurements. Figure 4c shows the measured and modeled air temperature profiles for the same day. As for CO2 and δ13CO2, the disagreement between modeled and measured air temperature is greater at 0500, 0700, and 2300 hours, which indicates a consistency between this tracer and the two others. Inspection of the measured temperature profiles at 0700 hours shows that turbulence is characterized as unstable within and above the canopy, and stable in the understorey. MuSICA, which only uses one turbulent parameter to describe both canopy and understorey turbulence, cannot account for this duality and switches from stable to unstable conditions without converging. At this time of the day the modeled sensible heat flux is dominated by the air storage term. For this reason, we think that the scalar profiles given by MuSICA are acceptable only when air storage in sensible heat is smaller than the sensible heat flux.
4.3. Determination of δr
Bowling et al.  determined the value of the respired CO2 signature δr using the Keeling model [Keeling, 1961]. In this model, the value of δr is defined as the intercept of the regression of δa versus 1/Ca during nighttime. Note that the determination of δr requires extrapolation far from the actual range of measurements, possibly leading to large errors and sensitivity to outliers. As an alternative, we determined δr as the “instant” slope of the regression between the product Caδa and Ca, as suggested by Bakwin et al. . We used an orthogonal distance regression [Press et al., 1992] to account for errors both on δa (0.3‰) and Ca (10 ppmv).
 During our isotope experiment 187 flasks were collected at nighttime (between about 1900 and 0700 hours). Inspection of the results reported in Table 1a shows that the value of δr obtained using the Keeling model is nearly equal to, and statistically as good as, that obtained using the instant slope model. This value (−26.8 ± 0.1‰) is also in close agreement with the measured bulk 13C isotopic composition of the various carbon reservoirs, i.e., soil organic matter and plant biomass (Table 1b).
Table 1a. Intercept (Respective Slope) of the Regression Between Ca and 1/δa (Respective Caδa and Ca) During the Night (Before 0700 Hours and After 1900 Hours) Using All Levels and All Time Steps or All Levels for Each Time Stepa
In the latter case, only the mean value (over all time steps) and its standard deviation are shown.
Keeling (Ca versus 1/δa) all levels: all time steps
−26.9 ± 0.1
Instant slope (Caδa versus Ca) all levels: all time steps
−26.8 ± 0.1
All levels: average time step
−27.1 ± 0.3
Table 1b. 13C Isotopic Composition of Canopy Needles and Collar, Understorey Leaves and Collar, and Soil Organic Matter at the Bray Site on 4 September 1997
Bottom: 0–1 year old needle
−28.7 ± 0.4
Bottom: 1–2 year old needle
−27.7 ± 0.3
Bottom: 2–3 year old needle
−27.3 ± 0.3
Top: 1–2 year old needle
−28.1 ± 0.3
−26.0 ± 0.5
−29.8 ± 0.5
−28.5 ± 0.7
Soil Organic Matter
−28.0 ± 0.3
 Two assumptions are at the origin of the Keeling model (or the instant slope model). First, we assume the existence of a “background” infinite reservoir of constant isotopic composition during the whole night. Second, we assume that all the respired carbon originates from the same source with unique isotopic composition δr.
 In order to test the constancy of δr during the night, we performed a Caδa versus Ca regression for each time step. The very dense vertical resolution of the sampling during this campaign made this possible. The results are encouraging as it is not possible to detect any temporal evolution in δr. The scatter between all time steps is small (standard deviation of 0.3‰) with a mean value (−27.1‰) close to the value obtained with the full data set (−26.8‰). This seems to indicate that the respired CO2 keeps a constant isotopic composition over the night.
 In order to test the uniqueness of δr we also made Caδa versus Ca regressions for each level. The results in Figure 5a show that the value obtained with the full data set (in gray in the figure) is actually smaller than any value obtained with a subset corresponding to one single level. This indicates that the intercept of the Caδa versus Ca regression also varies from one level to another because the background reservoir is probably not the same at each level. We also see in Figure 5a that the source of respired 13CO2 seems more enriched around 10–15 m and close to the ground than at any other level. Because the canopy layer is located around 11–17 m and the understorey is confined in the first meter above ground, this may indicate that the CO2 respired by canopy needles and understorey leaves is more enriched than the CO2 respired by the other sources (trunk, branches, and soil). The bulk 13C isotopic composition of the various organic matter reservoirs (leaves, needles, collar, and soil) have nearly the same value (around −28‰, see Table 1b). This implies that the CO2 respired by leaf elements has a different isotopic signature than whole-leaf dry matter. Such a situation has already been observed on coniferous needles [Brendel, 2001]. Indeed, leaves contain both structural carbon and newly fixed carbon (soluble sugars and starch) that may have a different isotopic composition [e.g., Le Roux et al., 2001]. At a short timescale (less than a day), the isotopic composition of carbon that has been newly fixed by a leaf is well correlated with the Cc/Ca ratio, i.e., the isotopic discrimination of the leaf [Lauteri et al., 1993]. Over night the carbon respired by a leaf is likely to have an isotopic composition closer to that of this newly fixed carbon than that of the whole-leaf dry matter.
 We used the MuSICA model to investigate this issue. We plotted in Figure 5b the δr values at each level obtained with the Ca and δa profiles given by the model. The latter is forced by the Ca and δa measurements at 25 m. The δr value at this level is not exactly the same in Figures 5a and 5b (−26.3 ± 1.6 and −26.5 ± 1.4‰, respectively) because in order to get continuous forcing variables over the whole night and run the model, we interpolated missing δa values at 25 m with the Caδa versus Ca linear regression used to get δr. The plot in Figure 5b was obtained with a constant and unique isotopic composition (fixed at −28‰) for all respiring plant and soil elements accounted for in MuSICA (i.e., 1-, 2-, and 3-year-old needles, trunks, and branches, understorey leaves, roots, and soil heterotrophs). As expected, the δr values vary smoothly from the value fixed at 25 m (−26.5‰) and a value close to −28‰ at the ground. They do not reproduce the observed air isotopic enrichment around 10–15 m and close to the ground. We modified the isotopic composition of the various respiring plant and soil elements in MuSICA and tried to retrieve this air enrichment within the two green vegetation layers. Within a realistic range of δ13C values (−28 ± 5‰) the model is unable to generate a δr profile as in Figure 5a. The model apparently does not match well enough the CO2 and δ13CO2 profiles within the vegetation during the night (Figure 4, between 1900 and 0700 hours). At these levels MuSICA apparently predicts too strong air mixing so that the air isotopic composition is not affected enough by the CO2 respired by leaves or needles. This also explains why the value at the ground is not exactly equal to −28‰. Warland and Thurtell  found that the turbulent transfer theory used in MuSICA could lead to an overestimation of the air mixing near the sources. They suggested an alternate model that should be tested in the future.
 In equations (4a) and (4b) δr represents the isotope signature of daytime nonfoliar respiration. When we estimate δr from nighttime profiles we assume that the isotopic signature for foliar and nonfoliar or daytime and nighttime respiration is unique. If foliar respiration at night has a different isotopic signature than nonfoliar respiration it is not quite correct to estimate δr from nighttime profiles. Foliar respiration at night represents about 1/3 of total respiration. Because Ca and δa measurements above the vegetation integrate all sources of CO2 below, they should be less affected by foliar respiration than any measurement performed within vegetation layers. The estimation of δr should then be performed only from Ca and δa measurements taken at levels above the vegetation in order to reduce the possible bias caused by foliar respiration. In what follows, we keep the value of δr estimated from all levels (−26.8 ± 0.1‰) because it is close to the value found at levels above the vegetation (25 and 38 m) and has much lower uncertainty due to the larger data set. Other campaigns with the same dense vertical resolution are strongly needed to confirm our results.
4.4. Determination of the Eddy Isoflux
 In order to retrieve a 10-Hz time series for δa and compute the eddy isoflux (equation (5)), we first need to determine the daytime linear regression between δa and Ca at 25 m (where the eddy flux is measured).
Bowling et al.  provided no theoretical justification for the existence of a linear relationship between δa and Ca but they rather convincingly verified its robustness empirically. In fact, one would expect a linear relationship to hold true only between the product Caδa and Ca. An observer placed at a given height above the canopy always measures gas concentration from different air parcels, or eddies, which originate from other heights. An arbitrary degree of mixing occurs, but in the absence of sources during the parcel transit, any rapid change detected in gas concentration relates to the vertical concentration gradient and to the parcel origin. In the case of two conservative tracers, here Caδa and Ca, the ratio of their concentration changes is preserved during mixing, and it is equal to the ratio of the two gradients. It is shown in Appendix B that, under the above conditions, the linear relationship between δa and Ca observed by Bowling et al.  is a good approximation of an exact linear regression between Caδa and Ca. It seemed therefore preferable to compute the eddy isoflux from a linear regression of Caδa and Ca, as was done for nighttime values to find the Keeling plot intercept.
 Writing Caδa = MCa + P leads to a simpler relationship (compared to equation (5)) between the CO2 eddy flux and the corresponding eddy isoflux:
 In the case where M = δr (and under the hypothesis that the storage terms can be neglected during the day) we cannot estimate FA and FR anymore as equations (4a) and (4b) become proportional and isotopic equilibrium (δa − ΔA = δr) is reached. Fortunately, isotopic equilibrium is unlikely to be satisfied at an hourly timescale. Indeed, ΔA (so as gc) reacts rapidly to plant water status and radiation changes [e.g., Le Roux et al., 2001] while δr is a time integrator of δa − ΔA. It must therefore be possible to use equation (13) to retrieve FA and FR.
 The values of M and P used in equation (12) were estimated from the CO2 and 13CO2 daytime measurements at 25 m (Table 2). Inspection of the results shows that the slope M used in equation (13) (−23.6‰) is actually far from the equilibrium value (−26.8‰), indicating that the partitioning exercise seems possible.
Table 2. Slope and Intercept of the Linear Regression Between Caδa and Ca Using Either the 25-m Level Only or the Four Levels Between 14 and 38 m
m or M
p or P
Bowling (δaVersus Ca)
−0.036 ± 0.002l
4.4 ± 0.7
14–38 m levels
−0.038 ± 0.001
5.2 ± 0.4
Instant Slope (CaδaVersus Ca)
−23.6 ± 0.8
(5.4 ± 0.3) × 103
14–38 m levels
−24.1 ± 0.4
(5.7 ± 0.1) × 103
 We only used the measurements at 25 m to determine M and P because it was the level at which the eddy flux was measured. We also computed the slope M of the Caδa versus Ca linear regression obtained at the other levels (Figure 6). We can see that the air near the ground is more in equilibrium than the air above the vegetation as the value of M gets closer to δr with decreasing height. This is due to soil respiration having a greater weight in the total CO2 source/sink strength near the ground. Therefore taking other lower levels to estimate M should bias the results by giving too much weight to the lower sources, resulting in lower values for M. Note, however, that if we take the four upper levels (between 14 and 38 m) we get values for M and P that are only 2 and 5% smaller than the values obtained with the 25-m level but with a smaller standard deviation (Table 2).
 From equation (13) (see also Appendix B) we can see that M is the ratio of the eddy isoflux to the eddy flux and is likely to change during the day. In Figure 7 we plotted these two eddy fluxes and their ratio, either predicted by MuSICA or estimated from measurements. The results have been bin averaged over the whole 22-day period. The eddy isoflux computed with equation (13) (solid circles) is in excellent agreement with MuSICA (solid line), especially in the afternoon (Figure 7a). This is also the case for the measured and modeled eddy CO2 flux (Figure 7b, see also Figure 3). It is therefore not surprising to see that the ratio of the two eddy fluxes given by MuSICA is rather stable in the afternoon and close to the value of −23.6‰ derived from the Ca and δa measurements at 25 m (Figure 7c). On the other hand, before noon and in the evening the model predicts rapid and large fluctuations of M with a strong day-to-day variability. The eddy isoflux can be seen as the difference of the isoflux and the isostorage. Both terms are likely to vary strongly in the morning and the evening as they depend on δa − Δa and turbulence, respectively. Therefore the variations of M predicted by MuSICA in the morning and the evening are likely to be real. Nonetheless, the amplitude given by MuSICA is probably amplified by numerical instability as we saw earlier that MuSICA encounters difficulties to converge when the sensible heat flux is dominated by the air storage term.
 In the light of Figure 7c we could think that the estimation of M and the Caδa versus Ca linear regression could be made with Ca and δa measurements performed in the afternoon only. In fact such a regression is inaccurate because Ca and δa variations are too small in the afternoon (not shown, but see Figure 8b below). Indeed, when only afternoon Ca and δa measurements are considered the resulting M value lies very far (less than −40‰) from the values given by MuSICA or the value of −23.6‰ obtained with all time steps. Even if it seems theoretically not fully satisfying, the morning values are crucial to determine M accurately. Increasing the accuracy of Ca and δa profiles in the afternoon may also overcome the problem.
4.5. Determination of the Isostorage
 CO2 storage is needed to compute NEE (right-hand side of equation (4a)). Similarly, the isostorage is needed to compute the isoflux (right-hand side of equation (4b)). The values of δa at all levels over the whole period are then necessary.
 CO2 measurements were available at all levels and over the 22-day period but 13CO2 measurements were only available over a 24-hour period. We then performed level-by-level linear regressions between daytime Caδa and Ca data. The slope of these regressions corresponds to the values plotted in Figure 6 and the regression at 25 m already gave us M and P.
 We used these regression outputs, the nighttime regression results (used to determine δr) and the CO2 measurements to construct continuous variations of 13CO2 at all levels and over the whole 22-day period. This allowed us to compute the “measured” isostorage. The resulting δa values at 25 m were also used to run the MuSICA model over the whole period.
Figure 8 shows the measured and modeled values of the isostorage and the resulting isoflux. The results have been bin averaged over the 22-day period. We can see that the agreement between model and measurements are good during the day except around 0800–1000 hours when the measurements seem to indicate a greater flush out of 13CO2 than the model. The same tendency is observed between measured and modeled CO2 storage and NEE (not shown). The fact that MuSICA has difficulties to capture the scalar profiles (and consequently, the storage terms) in the early morning may explain the disagreement. However, the measured NEE is computed as the sum of the measured eddy flux and the measured CO2 storage but the modeled NEE is independent of the modeled CO2 storage. It is therefore surprising to see that the model is unable to capture the NEE variations at this time of the day while it behaves well at other periods. This may indicate that the measurements (concerning the air storage or the eddy flux) are themselves erroneous at this time of the day. Overall it is difficult to know which isostorage, between the model and the measurements, is the most realistic.
4.6. Determination of the Canopy Conductance
 We evaluated the ability of the Penmann-Monteith equation to retrieve a canopy conductance gc. For this we applied equation (9) over the 22-day period using the energy and radiative flux measurements available at our site. The results are bin averaged over the whole period and are shown in Figure 9a. We also plotted the bulk canopy conductance predicted by the MuSICA model with its standard deviation over the period. The computation of this bulk canopy conductance from the modeled stomatal conductances of each leaf is not unique and two different definitions may result in large discrepancies [Finnigan and Raupach, 1987]. We chose the definition of Finnigan and Raupach because it is directly derived from the Penmann-Monteith equation which ensures conservation of the total latent heat flux (see Appendix C).
Figure 9a shows that the diurnal pattern is similar for both canopy conductances. However, we notice that the Penmann-Monteith equation gives bin-averaged gc values slightly smaller than the bulk canopy conductance given by the MuSICA model. It has to be pointed out that LE encloses not only transpiration from the vegetation but also soil evaporation, which should rather enhance the bulk canopy conductance from the Penmann-Monteith equation. Larger gc values of MuSICA compared to the Penmann-Monteith equation may be explained by discrepancies in the energy budget closure observed over the 22-day period. Indeed, the sum of the turbulent fluxes H and LE only represents 84% of the available energy Rn − G (not shown) which causes an underestimation of the bulk canopy conductance estimated with the Penmann-Monteith equation (see equation (9)).
Figure 9b shows the aerodynamic conductance ga computed according to equations (10) and (11). This conductance is 3–4 times smaller than the area-weighted average of the leaf boundary layer conductances (not shown, see Appendix C) but is still an order of magnitude greater than gc. The aerodynamic conductance ga therefore has a relatively small impact on the computation of ΔA and on the retrieval of FA and FR.
Figure 9c shows the bulk mesophyll conductance gm = 1/rm given by the MuSICA model. This bulk conductance is computed from leaf conductances at the leaf level in a way similar to the computation of gc (see Appendix C). In MuSICA the mesophyll conductance is set at 0.5 mol m−2 s−1 for understorey leaves and 0.125 mol m−2 s−1 for canopy needles [Loreto et al., 1992]. The resulting bulk mesophyll conductance varies from 0 to 0.5 mol m−2 s−1 (Figure 9c) because it has been weighted with leaf assimilation. We took the maximum value (0.5 mol m−2 s−1) in equations (7) and (8) to estimate FA and FR because it corresponds to the average midday value. Note that Bowling et al.  neglected the mesophyll resistance 1/gm compared with the bulk canopy resistance 1/gc. In their case the expression for reduces to = a = 4.4‰ and equation (8) becomes −FA = gc(Ca − Cc). Such a simplification is not possible in our case because gm is only 2–3 times as large as gc.
4.7. Retrieval of FR, FA, and Δa
 First, we found it important to illustrate the difference between FR and TER (or FA and GPP). The values of FR and FA (solid line) and TER and GPP (dashed line) obtained with MuSICA over the 22-day period are shown in Figures 10a and 10b. As for the preceding variables the results have been bin averaged. TER estimates can also be obtained from a regression of nocturnal NEE versus soil temperature, but for our study, such a regression was inaccurate because of the small range of soil temperature during the 22-day period. However, using the regression of Berbigier et al.  (obtained at the same site after 2 years of eddy-flux measurements) would give almost the same TER and GPP curves (not shown). We can see in Figure 10a that FR is 30–50% smaller than TER during the day, with little day-to-day variability. The difference between FA and GPP is proportionally much smaller and within the range of the day-to-day variability in FA. This is because TER mainly depends on soil temperature and moisture which vary slowly during the period of study, while GPP depends on several environmental factors such as radiation, air VPD or wind speed, and is likely to vary strongly from one day to the next. It is clear from Figure 10a that it is not possible to validate the method of Bowling et al. (that separates NEE into FR and FA) by comparing the results to TER and GPP estimates. A model such as MuSICA, which gives independent FA and FR estimates, is necessary to validate this method.
 The fractionation factor ΔA is a linear function of FA (see equations (6) and (8)) so that equation (4b) can be rewritten as a quadratic equation in FA [Bowling et al., 2001]. This equation is solved for FA according to Press et al.  and FR is given by equation (4a). The resulting FR and FA values for the 22-day period have been bin averaged and plotted in Figures 10a and 10b (solid circles). The agreement with the FR and FA values predicted by MuSICA is rather good, especially in the afternoon where it remains within 15–20% at most time steps. In the morning (around 0800−1000 hours) FR values given by equation (4a) are overestimated compared to those given by MuSICA and become closer to TER. However, this disagreement lies within the day-to-day variability of FA (Figure 10b). The reason for this disagreement is explained below.
 As mentioned by Bowling et al.  the EC/flask method is very sensitive to gc. Indeed, when we take gc given by MuSICA rather than the Penmann-Monteith equation this gives quite different FR and FA values (not shown). A better agreement is obtained when we use simultaneously gc and gm given by MuSICA. The resulting FR values (open circles in Figures 10a and 10b) are then close to those given by MuSICA, especially in the midafternoon (1200–1700 hours) where the agreement approaches 5–10%, but remains overestimated and closer to TER in the morning.
 In fact the quadratic equation of FA may sometimes have no real solution. In this case FR is not computed and not accounted for in the bin averaging. Such a situation occurs when δa − ΔA is close to δr. We plotted in Figure 10c the bin-averaged δa − ΔA values given by MuSICA and by equations (6) and (8). The model predicts that isotopic equilibrium (i.e., δa − ΔA = δr) is more often satisfied in the morning (around 0900–1100 hours) and before sunset (around 1800 hours). The bin-averaged δa − ΔA values given by equations (6) and (8) are therefore not representative of the whole period and should not be trusted at this time of the day. In other words, the EC/flask method works better at certain times of the day than others. The period at which it works best is in the midafternoon (around 1400–1600 hours), when ΔA takes its minimum absolute value and the isotopic disequilibrium is strong. Fortunately, FR has a small amplitude during daytime so that the value at 1400–1600 hours is representative of the whole day.
 This result and other results from the preceding sections help us formulate an efficient and cost-effective sampling strategy.
4.8. Retrieval of FR and FA From a Data Subset
 Our objective here is to consider the possibility to retrieve FR and FA on a routine basis with the EC/flask method of Bowling et al. . We saw that with the full data set of isotopic measurements (341 flasks over a 24-hour period) we were able to retrieve correctly FR and FA over a longer period (within 15–20%). However, this experimental setup is obviously too heavy to be implemented on a routine basis. The next step is to determine a subset of isotopic data that would allow us to retrieve FR and FA (or rather their mean daytime value) with a similar accuracy.
 Nighttime isotopic measurements are needed to estimate δr. We saw that the estimation of δr depends on sampling: the overall nighttime data set gives a value of −26.8‰ but the same data set gives different values when it is subsampled by levels (−26.3‰ at 25 m) or by time steps (−27.1‰ on an average). However, the scatter between δr values at different time steps remains within the range of measurement errors (0.3‰). We can therefore imagine to use only Ca and δa measurements at one or two time steps only but from several levels. It seems preferable to reduce the number of levels within the vegetation in order to reduce the possible impact of foliar respiration on the determination of δr. If we only take one isotopic measurement by vegetation layer, i.e., at 25 m, within the canopy, below the canopy, in the understorey, and at the ground, we then have to analyze only 5 or 10 flasks instead of the 187 flasks collected at night during our 24-hour campaign.
 Daytime isotopic measurements are used to estimate M and the corresponding eddy-isoflux ,and to compute the isostorage during the day. The estimation of M is made with the isotopic measurements at 25 m only. Several time steps are therefore needed to get an accurate value, but four or five isotopic measurements are sufficient. We saw in the preceding section that FR had a small amplitude during daytime. We can therefore estimate FR at times of the day when the EC/flask method works best (in midafternoon, when the ecosystem is far from isotopic equilibrium) and extrapolate the results to the whole daytime period. We pointed out that M could not be determined from afternoon values only because the range of variation in Ca and δa is too small at this period of the day. Such a behavior is general and has been observed at a variety of sites [e.g., Buchmann et al., 1997]. Our subset of isotopic data should therefore contain 13CO2 measurements in the morning (to determine M) and in the afternoon (when the EC/flask method works best).
 In theory, isostorage requires 13CO2 measurements at all levels in order to perform linear regressions between Caδa and Ca, and to get continuous δa values at all levels. As can be seen in Figure 6, the regression differs from one level to the next. As a sensitivity test, we computed the isostorage from δa values estimated with the regression found at 25 m only. The resulting isostorage is not significantly different from the isostorage plotted in Figure 8b (not shown) and leads to almost the same FR/FA estimates. Therefore the isotopic measurements at levels other than 25 m do not seem crucial during daytime. The four or five isotopic measurements during the day should therefore be sufficient to estimate both M and the isostorage. By comparison, for our 24-hour campaign, we collected 14 flasks at 25 m during daytime and the same amount of flasks was collected at the other 10 levels.
 We subsampled our data set by taking only two nighttime 13CO2 profiles (at 2400 and 0100 hours) with only five levels (25, 14, 6, 0.7, and 0.01 m) and four daytime 13CO2 values (0700, 0800, 1400, and 1500 hours). We then obtained δr = −27.3 ± 0.6‰ and M = −23.7 ± 1.0‰, compared to −26.8 ± 0.1‰ and −23.6 ± 0.7‰ with the full data set, respectively. The isostorage was also not significantly different than that computed with the full data set.
 We then partitioned NEE into FR and FA. Results are presented in Table 3 in terms of mean daytime nonfoliar respiration 〈FR〉. We can see that values obtained with our subset of data are not very different from those obtained with the full data set. In all cases they are about 15–20% smaller than the value given by MuSICA, which must be considered as the order of magnitude of the accuracy of the EC/flask method.
Table 3. Mean Nonfoliar Respiration Over the 22-Day Period Predicted by Different Approaches (PM = Penmann-Monteith Equation) and Sampling Strategiesa
〈FR〉, g C m−2 d−1
In parentheses we give the results when the mean is computed with only four values during the day (0700, 0800, 1400, and 1500 hours), assuming that FR does not change much during the day.
Full data set
gc (PM) with gm = 0.5 mmol m−2 s−1
gc (MuSICA) with gm(MuSICA)
Subset of data
gc (PM) with gm = 0.5 mmol m−2 s−1
gc (MuSICA) with gm(MuSICA)
gc (PM) without gm
gc (MuSICA) without gm
 Finally, we tested the effect of neglecting the mesophyll resistance 1/gm compared with the bulk canopy resistance 1/gc on the retrieval of FA and FR. Indeed, the estimation of a bulk mesophyll conductance for a given ecosystem is not easy and very few data are available in the literature. Table 3 shows that the 〈FR〉 value is in this case much greater than before (around 6 g C m−2 s−1 depending on the choice of gc) and than the average TER given by MuSICA (5.1 g C m−2 s−1). This is because the total conductance in equation (8) and thus FA are then overestimated. Such a simplification is therefore impossible in our case and we need to prescribe a value for gm to perform the partitioning. The results may be different at other sites with a greater mesophyll conductance. Nevertheless, before applying the EC/flask method to partition FR and FA at a given site one must have an idea of the value of the mesophyll conductance, as compared with the stomatal conductance.
 In this paper we investigated the possibility to estimate FR and FA at one FluxNet site from continuous CO2 flux and concentration measurements and intensive 13CO2 measurements. For this we applied the EC/flask method of Bowling et al.  and used the multilayer model MuSICA as a perfect simulator to test each underlying hypothesis and evaluate the partitioning. The idea was to apply this method on a routine basis, i.e., by collecting less isotopic measurements at each campaign, but more regularly during one growing season. Our objective was then to formulate an efficient and cost-effective strategy to get the best subset of isotopic measurements to perform the partitioning of NEE into FR and FA. The method can be decomposed into different steps (Figure 1).
 First, we needed to estimate the daytime isotopic signature δr of nonfoliar respiration. For this we made a Caδa versus Ca linear regression using measurements collected during one night at different levels above and within the vegetation, and identified δr as the slope of this regression. The value of δr estimated with the full data set was −26.8 ± 0.1‰, in close agreement with the isotopic content of soil organic matter and plant biomass (Table 1b). Such determination of δr relies on the assumptions that δr is constant with time and that foliar and nonfoliar or nighttime and daytime respiration rates have the same isotopic signature. Making a regression for each time step or at each level revealed that the value of δr changed little during the night (Table 1a), but the slope of the regression appeared to differ significantly from one level to the next (Figure 5a), with higher values in the vegetative layers. Such a situation would occur if foliar respiration was enriched compared to nonfoliar respiration. In this case it would be problematic to estimate δr with our method as one of the underlying assumptions would not hold. Other campaigns are therefore needed to confirm this result. To go one step further we also ran MuSICA with a range of isotopic signatures for the CO2 respired by leaf elements. In all simulations the model predicted Ca and δa values that never lead to such vertical variations of δr, as those obtained with the experimental data. One possible explanation is that the turbulent transfer module used in MuSICA overestimates the air mixing in the vegetative layers as has already been observed in a previous study [Warland and Thurtell, 2000]. Other turbulent transfer theories need to be tested to explore this possibility. We conclude that despite the dense vertical and temporal resolution of this experimental study and the refinement of the MuSICA model, it was not possible to confirm that the assumptions underlying the determination of δr were verified at our site. Assuming that they are, a cost-effective sampling strategy to estimate δr is to measure one or two 13CO2 profiles during the night with four or five levels only, preferentially not in the vegetative layers.
 Secondly, we had to estimate the eddy isoflux. For this we showed that the use of equation (13) was more accurate than its first-order approximation (equation (5)) because it is Caδa and not δa alone that is linearly related to Ca (see Appendix B). We then made a Caδa versus Ca linear regression using daytime measurements at 25 m to estimate the slope M to be used in equation (13). We used the measurements at 25 m only because it is the level at which the eddy flux was performed. We showed that using other levels (not too close to the canopy top) would not lead to very different values of M (Figure 6 and Table 2). We also showed that the estimation of M could not be performed without a certain range of variations of Ca and δa and that the early morning values are crucial to get an accurate value for M. For this reason we conclude that the best strategy to estimate M is to perform 13CO2 measurements at one level (where the eddy flux is measured) and in the early morning (around 0700–0800 hours solar time) and in the afternoon (around 1400–1600 hours).
 Thirdly, we needed to estimate the isostorage. For this we used the CO2 profiles and the regressions used to determine δr and M to construct a continuous data set of 13CO2 values. The use of a regression level by level during the day (which was possible because 13CO2 measurements were performed at the same 11 levels than CO2 measurements) changed only slightly our estimates of the isostorage, especially in the midafternoon. The regressions giving δr and M are therefore sufficient to retrieve a continuous data set of 13CO2 values and estimate the isostorage, as long as we perform continuous CO2 measurements at different levels.
 Fourth, we had to estimate the bulk canopy and mesophyll conductances. The Penmann-Monteith equation is quite robust to estimate gc and we verified it with our data set. The bulk mesophyll conductance is difficult to estimate but appears to play an important role in the partitioning exercise. It is therefore crucial to get an estimate of the relative importance of the mesophyll conductance compared with the stomatal conductance if we want to get accurate estimates of FR and FA.
 With our full data set we were able to retrieve FA and FR values in agreement with the MuSICA model within 15–20%. We showed that the EC/flask method works better in midafternoon when ΔA takes its minimum absolute value and isotopic disequilibrium is strong. Using the subset of data allowed us to retrieve average FA and FR values that agree with MuSICA within 15–20% also. This was made possible because FR does not have a marked diurnal cycle.
 This study allowed us to define the best cost-effective sampling strategy to estimate FR and FA from continuous CO2 flux and concentration measurements, and intensive 13CO2 measurements. In the future we need to check whether the conditions of occurrence of isotopic disequilibrium vary or not with species or throughout the growing season. It is clear that the minimum of ΔA should always occur in midafternoon when we have the highest levels of vapor pressure deficit. Indeed, this strong evaporative demand forces the stomata to close but little affects the rate of photosynthesis so that the ratio Cc/Ca and ΔA are lower. However, the daily minimum of ΔA, and the values of δa and δr should vary throughout the season, and some days isotopic disequilibrium may never occur. Additional studies at other seasons and other sites are now needed to check whether the retrieval of FA and FR can really be performed throughout the season within a 15–20% confidence interval.
A1. MuSICA and the Transport of 13CO2
 The multilayer multileaf soil-vegetation-atmosphere transfer model MuSICA is extensively described elsewhere [Ogée et al., 2003]. Equations for the transport of 13CO2 have been added for the present study and are presented here.
A1.1. Turbulent Transfer in MuSICA
 The total air concentration of a given scalar (for example Ca,k for CO2) at any level zk is computed with a Lagrangian turbulent transfer scheme summarized in the equation [Baldocchi and Harley, 1995; Raupach, 1989a]:
where Ca,r (μmol m−3) is the total CO2 concentration at a reference level zr above vegetation, Sj (μmol m−3 s−1) is the total CO2 source/sink density of vegetation layer j with thickness Δzj (m), n is the number of vegetation layers, and Dkj (s m−1) is the turbulent dispersion matrix. The latter depends solely on turbulence statistics and is computed according to the localized near-field theory [Raupach, 1989b]. F0 (μmol m−2 s−1) is the total CO2 efflux that emanates from the forest floor.
 In each canopy layer we distinguish 12 types of big leaves (or big shoots) according to their age (1-, 2-, or 3-year-old), sun exposure (sunlit or shaded), and water status (wet or dry). In the understorey layer we distinguish only four big leaves because they belong to a single age class. The CO2 source/sink density of vegetation layer j with thickness Δzj can be expressed as:
where ℓtype,j (m2 m−3)is the leaf area density of the big leaf of type “type” in layer j, An,type,j (μmol m2 s−1) is its net CO2 exchange rate with surrounding air, and Fbole,j (μmol m2 s−1) is the bole respiration rate. The summation in equation (A2) is restricted to dry big leaves only because wet leaves are not supposed to exchange CO2 with the atmosphere.
Ca,k can be decomposed into various isotopic concentrations. For each of these an equation similar to equation (A1) applies. For example, for 13CO2:
where superscript “13” denotes the same quantities as for the total scalar concentration but for the 13CO2 isotopic concentration only. In δ notation we have:
where δj represents the isotopic composition of source Sj and is defined by (1 + δj) RPDB = Sj13/Sj and (1 + δ0) RPDB = F013/F0 where RPDB is the isotopic composition of the Pee Dee Belemnite standard. It usually depends linearly on the air isotopic composition of the air (see below) so that we can write:
 This equation can be solved in deltas. The expressions of the coefficients Akj and Bk are related to coefficients aj and bj by:
where εkj equals 1 if k = j, and 0 otherwise.
A1.2. Expression of the Coefficients aj and bj for 13CO2
 The CO2 source/sink density of vegetation layer j is given by equation (A2). For 13CO2 we have:
 The same notations as in equation (A2) are used but with superscript 13 for 13CO2 assimilation and bole respiration rates.
 The 13CO2 assimilation rate of a dry assimilating (gs > 0) leaf is computed according to Farquhar et al.  and the 13CO2 exchange rate of a dry nonassimilating (gs = 0) leaf is simply expressed as the product of the respiration rate and the 13CO2/CO2 isotopic composition of “freshly respired sugars” (δtype,j). The 13CO2 bole respiration rate in layer j is also expressed as the product of the bole respiration rate (Fbole,j) and the 13CO2/CO2 isotopic composition of freshly respired sugars (δbole,j). We then get:
where ΔA,type,j is given by equations similar to equations (6) and (7). If we decompose the soil CO2 efflux into microbial and root respiration (F0 = Fmicrob + Froot) with two different isotopic compositions (δmicrob and δroot) we get:
 In the present version of MuSICA the isotopic compositions δbole,j, δtype,j, δroot, and δmicrob are prescribed, and not allowed to change over time.
A1.3. Parameterization of MuSICA
 The parameterization of MuSICA is that used by Ogée et al.  at the same site, except that soil respiration at 15°C has been reduced by 50%. This modification was necessary to account for the effect of low soil water levels on soil respiration [Ogée et al., 2003]. In addition, leaf mesophyll conductances have been included in the model because the discrimination factors ΔA,type,j depend on chloroplastic, not internal, CO2 concentration. During the computation of leaf assimilation (An,type,j) these conductances are set to an infinite value for keeping the model consistent with the set of values used for the parameterization of the photosynthesis model, all established on an internal, not chloroplastic, CO2 basis. The model then relates the chloroplastic CO2 concentration to An,type,j and the internal CO2 concentration.
Appendix B:: Relationship Between Cδ and C
 The surface boundary layer above vegetation is divided into two regions: the inertial sublayer above a level conventionally referred to as z* (on the order of 2 to a few times the vegetation height h) and the roughness sublayer below this level.
 Using similarity theory principles Cellier and Brunet  found that, for any atmospheric tracer X, the vertical gradient above vegetation (h < z< z*) can be expressed as:
where X* is the scalar turbulent flux normalized by U*, ϕx and ζ are a nondimensional stability function and a stability parameter, respectively, and k is the von Karman constant (0.4).
 The stability parameter ζ is usually taken equal to h/L in the roughness sublayer, where L is the Obukhov length scale [Jacobs et al., 1992; Leclerc and Beissner, 1990; Shaw et al., 1988]. In this case the gradient dX/dz is constant between h and z*. For two scalars, here Ca and Caδa, this means that their gradients are proportional in this region:
 We should therefore express Caδa in terms of Ca to compute the eddy isoflux. Note that the linear relationship between Caδa and Ca should not depend on atmospheric stability (assuming that the stability function is the same for both scalars) but only on the ratio of the two scalar turbulent fluxes. If we neglect storage terms in equation (4) (which is possible in midafternoon for instance), the coefficient M is then equal to δr + (δa − ΔA − δr)FA/(FA + FR).
 Writing d(δaCa) = δadCa + Cadδa we also get:
 Over the range of variation in atmospheric CO2 concentration, 1/Ca can be considered as nearly constant. At this first-order approximation we then have proportionality between Ca and δa gradients, as was empirically assumed by Bowling et al. , and we can also express δa in terms of Ca to compute the eddy isoflux.
 These linear relationships should actually vary from one time step to the next and a different value for M should be used to compute the eddy isoflux at each time step. Yet a single linear relationship seems to hold during the full daytime period (Table 2; see also Bowling et al. ). This is partly explained by the fact that δa − ΔA is close to δr and steady for most of the day (Figure 10c).
Appendix C:: Bulk Canopy and Mesophyll Conductances
 The Penmann-Monteith equation at the canopy scale is:
 The primes denote conductances for water vapor instead of CO2. This equation can also be applied at each big leaf within the canopy:
where gb,type,j and gs,type,j are the boundary layer and the stomatal conductances of big leaf of type “type” in layer j, respectively. If we assume that turbulence is well mixed then Da,j in equation (C2) can be replaced by Da. Then in the limit of potential evaporation (gc → ∞, gs,type,j → ∞), identification of the terms in Da and Rn − G in equations (C1) and (C2) leads to [Finnigan and Raupach, 1987]:
 Hence ga and Rn − G are simply the sum of their area-weighted counterparts at the leaf scale. We then computed gc from equation (C1) (see equation (9)), and substituting for Rn − G, ga, and LE in terms of leaf variables, from equations (C2) and (C3).
 The bulk mesophyll conductance is computed in the same framework. Net assimilation FA is given by equation (8) in terms of bulk conductances. In MuSICA this flux is computed according to:
 Assuming that turbulence yields to well-mixed conditions we replace Ca,j in equation (C4) by Ca. Then the identification of the terms in Ca in equations (C4) and (8) leads to an expression for the bulk mesophyll resistance rm in terms of leaf variables.
 The senior author was supported by a postdoctoral fellowship from the CNRS. This work was supported by the French programs AGRIGES and PNRH jointly founded by the BRGM, CEMAGREF, INRA, INSU/CNRS, IRD, and Météo-France. The authors wish to acknowledge the contributions made by Bernard Ladouche and Antoine Millet to the experimental setup and the isotopic sampling.