Seasonal and vertical variations in soil CO 2 production in a beech forest : an isotopic flux-gradient approach

Soil CO2 efflux results from the transport of CO2 from several respiration sources within the soil profile. A flux – gradient approach (FGA) was used to assess the vertical profile of CO2 production (P_CO2) and its isotopic composition (δ 13 P_CO2) from the measurement of the vertical profile of CO2 concentration and CO2 isotopic composition combined with soil CO2 and δ 13 CO2 effluxes. Variations in P_CO2 and δ 13 P_CO2 within different soil layers were analyzed at different time scales. In the first soil layers, P_CO2 was probably underestimated and δ 13 P_CO2 overestimated when CO2 transport was not 15 solely diffusive. At the seasonal scale, a vertical gradient of P_CO2 temperature sensitivity was observed. At the within-day scale, variations in soil temperature were too weak to explain the strong variations in P_CO2. At the daily time scale, δ 13 P_CO2 of sources located between -10 and -20 cm depth was well correlated with the canopy inherent water use efficiency (IWUE) measured the day before. The strong correlation with IWUE argues in favor of an actual connection between canopy activity and soil autotrophic production. Moreover, including SWC of the current day as a second variable improved the 20 linear regression between δ 13 P_CO2 and IWUE of the previous day, together explaining 76% of the daily fluctuations in δ 13 P_CO2. This highlights the actual contribution of both autotrophic and heterotrophic sources to soil P_CO2. The method used gave consistent and promising results even if we could not disentangle the respective contribution of autotrophic and heterotrophic sources to CO2 production as the differences in their isotopic composition were too small and fluctuated too much. In addition, CO2 transport by turbulent advection and dispersion will need to be considered for the top soil layer. 25


Introduction
Soil CO 2 efflux (F S ) is the major component of CO 2 emissions in terrestrial ecosystems (Ryan and Law, 2005) and represents 60% to 80% of the total respiration in forest ecosystems (Granier et al., 2000;Janssens et al., 2003;Law et al., 1999).
Accurate evaluations of F S and of its response to environmental factors are essential for predicting changes in the terrestrial carbon balance (Ryan and Law, 2005).To better characterize and model this flux, it is essential to understand the multiple complex processes contributing to F S (Subke et al., 2006).Although several empirical models have been used to describe the response of F S to soil temperature and soil water content, which are the main drivers accounting for its temporal variations at a seasonal scale (Davidson et al., 1998;Epron et al., 1999;Janssens and Pilegaard, 2003), further efforts are required to better understand the short-term dynamics of F S (Goffin et al., 2014;Moyes et al., 2010;Vargas et al., 2011Vargas et al., , 2012)).
F S is the result of CO 2 production (P_CO 2 ) in the soil through respiration of two main types of sources (autotrophic and heterotrophic) and of CO 2 transport up into the atmosphere (Fang and Moncrieff, 1999).The autotrophic sources include the respiration of roots and rhizospheric microorganisms while the heterotrophic sources are related to soil microorganisms decomposing soil organic matter (Epron, 2009;Subke et al., 2006).Both the autotrophic and heterotrophic components of the soil CO 2 efflux have their own responses to their multiple drivers (Boone et al., 1998;Epron et al., 2001;Suleau et al., 2011).In consequence, soil CO 2 efflux is dependent on soil temperature and moisture (Davidson et al., 1998), on soil porosity and tortuosity (Werner et al., 2004), on air pressure and turbulence fluctuations at the soil surface (Maier et al., 2012), on the quality and quantity of decomposable organic substrates (Conant et al., 2011) and on the soil microorganism community (Karhu et al., 2014).Moreover, several studies have shown evidence of a link between photosynthesis and soil CO 2 efflux (Kuzyakov and Gavrichkova, 2010;Risk et al., 2012;Wingate et al., 2010).Stable isotopes have become a useful tool in understanding the complexity of the processes involved in soil CO 2 efflux and in assessing the relative contributions of autotrophic and heterotrophic sources (Bowling et al., 2008;Marron et al., 2009;Prévost-Bouré et al., 2008).Variations in the C isotopic composition of F S (δ 13 F S ) have been related to soil moisture, temperature, rain events or vapor pressure deficit (Bowling et al., 2002;Ekblad et al., 2004;Fessenden and Ehleringer, 2003;Wingate et al., 2010).The latter relationship is part of the link between δ 13 F S and stomatal conductance or photosynthesis (Ekblad and Högberg, 2001;Lai et al., 2005;Bowling et al., 2008).
Many of these studies consider that the CO 2 released by the soil surface corresponds to the amount of CO 2 produced simultaneously within the soil, and that δ 13 Fs represents the actual isotopic signature of the mixture of all the CO 2 sources.However, CO 2 can be stored during its transport towards the soil surface, thus inducing differences between P and F S .In addition, CO 2 transport is driven mainly by diffusion (Davidson et al., 2006b;Pumpanen et al., 2008) and some fluctuations in the fractionation rate can occur during this CO 2 diffusion (Cerling et al., 1991).This may induce differences between the isotopic composition of CO 2 production (δ 13 P_CO 2 ) and δ 13 F S (Moyes et al., 2010).As a consequence, a more precise understanding of the processes underlying CO 2 efflux requires formally separating production and transport mechanisms within the vertical soil profile.As the main biotic (roots, microorganisms) and abiotic (soil temperature, soil water content, Biogeosciences Discuss., doi:10.5194/bg-2016-194, 2016 Manuscript under review for journal Biogeosciences Published: 17 May 2016 c Author(s) 2016.CC-BY 3.0 License.substrate quality and quantity) drivers influencing P_CO 2 present a strong vertical variability through the soil profile (Davidson et al., 2006b), the analysis of the vertical distribution of P_CO 2 sources is also essential to evaluate the vertical partitioning of the subsurface CO 2 processes (Davidson et al., 2006b;Goffin et al., 2014;Jassal et al., 2004;Pumpanen et al., 2003).However, vertical variability has seldom been taken into account.
The fluxgradient approach (FGA - Jong and Schappert, 1972) has already been used to assess the vertical profile of P_CO 2 and δ 13 P_CO 2 from the measurement of the [CO 2 ] vertical profile and its isotopic composition, F S and δ 13 F S (Goffin et al., 2014).All these variables can be recorded simultaneously (Parent et al., 2013), thus providing insights into the mechanisms affecting production and transport.
Our objectives were, first, to quantify the contribution of the different soil layers to CO 2 production and to its isotopic signature, and secondly, to examine the variability of these contributions at different time scales.We used the FGA approach to analyze and understand the constraints on vertical and seasonal variations in P_CO 2 and δ 13 P_CO 2 .We further related the seasonal variations to soil temperature and soil water content.We then investigated the impacts of canopy processes on daily variations in δ 13 P_CO 2 .The autotrophic signal was tracked up in soil CO 2 production P_CO 2 , thanks to the isotope composition of trunk respiration, the gross primary production and the evapotranspiration measured by a nearby eddy flux tower.

The fluxgradient approach
When the soil is considered as a one-dimensional structure (horizontal homogeneity), the CO 2 production (P_CO 2 , µmol m -3 s -1 ) at each depth (z, m) is derived from the corresponding one-dimensional mass balance equation for CO 2 : [1] where is the air-filled porosity (m 3 m −3 ), [CO 2 ] is the CO 2 concentration by m 3 of soil (µmol m −3 ), F is the CO 2 vertical flux (µmol m −2 s -1 ), t is the time (s) and z is the depth (m) for which all the variables of Eq. 1 are considered.
We divided the soil profile into five-centimeter-thick sections.Each section was characterized by a set of physical parameters (effective soil diffusion coefficient, porosity) and by environmental conditions (soil water content SWC, soil temperature T, [CO 2 ]).In each section i, P_CO 2 was calculated using the discrete form of Eq. 1: [2] where is the storage flux (µmol m -3 s -1 ), and F top and F bot (µmol m −2 s -1 ) are the gas fluxes transported through the upper and lower limits of the section, respectively.
Because diffusion was the only transport mechanism considered (see discussion), the flux (F) is expressed by Fick's first law: Biogeosciences Discuss., doi:10.5194/bg-2016Discuss., doi:10.5194/bg- -194, 2016 Manuscript under review for journal Biogeosciences Published: 17 May 2016 c Author(s) 2016.CC-BY 3.0 License. [3] [4] where Ds is the effective soil diffusion coefficient (m 2 s −1 ), corresponds to the harmonic mean value between the Ds of the x ( ) and y ( ) sections and Δz is the section thickness (m).
How we determined , and is presented in the following sections.
Eq. 2-4 were applied successively to 12 CO 2 and 13 CO 2 with their respective concentration and soil diffusion coefficient ( and ) to determine the production of these two isotopologues ( 12 P_CO 2 and 13 P_CO 2 ).For each section, total production ( ) and its isotopic composition (δ 13 P_CO 2 i , expressed in ‰) were calculated as follows: [5] δ [6] where R std is the isotopic ratio of the V-PDB reference standard.

Site description
The experiment was conducted in the Hesse beech forest located in north-eastern France (48°40' N, 7°05' E).The mean annual temperature (1997-2014) is 10.3°C and the mean annual precipitation is 979 mm.The soil is a Stagnic Luvisol (FAO, 2006) with a pH of 4.9 and containing 10 kg of organic carbon per m².A more detailed description is given by Granier et al. (2000).
The five-centimeter-thick sections in the FGA were part of three distinct layers in the soil vertical profile: [1] 0 to -10 cm, [2] -10 cm to -20 cm and [3] -20 to -40 cm (Fig. 1).The two first layers contained each one third of total root biomass according to the root vertical profile (Peiffer et al., 2005).The soil texture is silt loam with 22% of clay in the first 20 centimeters and 34% below.

Field measurements
2.3.1.Tree trunk CO 2 efflux (F t ), soil CO 2 efflux (F s ) and their isotopic signatures (δ 13 F t and δ 13 F s ) We used steady-state flow-through chambers (Marron et al., 2009;Plain et al., 2009)  [7] where F x represents F t or F s (µmol m -2 s -1 ), [CO 2 ] in and [CO 2 ] out represent the CO 2 concentrations (µmol mol -1 ) at the inlet and outlet of the chamber respectively, Pa is the atmospheric pressure (Pa), is the airflow rate through the chamber (m 3 s - 1 ), S is the soil or trunk surface inside the chamber (m²), T is the air temperature (K), and 8.314 J mol −1 K -1 is the ideal gas constant.
Soil chambers were made of stainless steel and allowed the enclosure of 314 cm 2 of soil.The chambers were composed of a 12.5-cm-high collar covered with mobile lids.Six collars were installed and every week, two of the four lids were moved to free collars in order to prevent a permanent soil covering.Consequently, each week's data set is composed of measurements from different combinations of four collars.To achieve a homogeneous time series, a gap filling procedure was performed for each collar during the periods when no measurements were conducted on it.This procedure is based on linear regressions between the different collar measurements (Goffin et al., 2014).The time series for each collar was compared with the time series of all the other collars and the linear equation from the best regression was chosen for gap filling.Mean F s and δ 13 F s were estimated as the average values of all the collars after gap filling.
F t and δ 13 F t were measured using two trunk chambers set up at the base of two trees (10 cm above the ground).Trunk chambers consist of a flexible polymethyl methacrylate cylindrical structure placed around a trunk portion 20 cm long.Air tightness is ensured by two rubber seals (at the top and bottom of the structure).The trunk chambers were covered with an insulated aluminum sheet to avoid light and any increase in temperature.The two trunk-and four soil-chamber effluxes were measured sequentially every 30 minutes.

Profiles of [CO 2 ], δ 13 C-CO 2 , SWC and T
We measured the soil CO 2 concentration [CO 2 ] and its isotopic signature δ 13 C-CO 2 profiles using a system set up by Parent et al. (2013) based on a membrane tube technique (Flechard et al., 2007;Gut et al., 1998) which allows gas concentration equilibrium between the internal and external atmosphere.In October 2009, two parallel trenches were dug and four polypropylene tubes (1.5 m long) with gas-permeable porous walls (Accurel PPV8/2) were inserted horizontally through the soil between the trenches and spaced horizontally 40 cm apart from each other at depths of 0 (just under the litter), 5, 10, 20 and 40 cm.In July 2011, four additional Accurel tubes were dropped on the litter layer.The porous tubes were extended with Synflex® tubing.The four Synflex® tubes coming from one depth were connected together at their two ends that were also connected to form one closed loop per depth.In each closed loop system, the temporal changes in [CO 2 ] were continuously measured by an infrared CO 2 analyzer (GMT 222 Vaisala Oyj,Helsinki,Finland).Biogeosciences Discuss., doi:10.5194/bg-2016-194, 2016 Manuscript under review for journal Biogeosciences Published: 17 May 2016 c Author(s) 2016.CC-BY 3.0 License.
A small amount of air was sampled from each closed loop sequentially every 30 minutes with a solenoid-valve selection system.These samples were then diluted with zero-CO 2 air before being passed through the TDLAS for δ 13 C-CO 2 measurement.To compensate for the pressure deficit caused by sampling air from the closed loops, the same amount of fresh air was injected at a point located before the passage into the Accurel tube.Previous tests have demonstrated the efficiency of this procedure (Parent et al., 2013).The TDLAS was calibrated every 5 min with three standard gases covering the range of [CO 2 ] and δ 13 C-CO 2 values encountered during the sampling campaign.Parent et al. (2013) provide more details about this system and the tests proving its reliability.
We used thermocouples (constantan-copper) to record the temperature profile every 30 minutes at 0, 5, 10, 20 and 40 cm in depth and volumetric soil moisture sensors inserted horizontally at 5, 10, 20 and 40 cm depth (Theta Probe ML1, Delta-T Devices, Cambridge UK) to determine the SWC profile every 30 minutes.Output from the probes was corrected according to a site-specific calibration which was performed in the laboratory.
Continuous vertical profiles of the variables ([CO 2 ] and δ 13 C-CO 2 , T and SWC) were obtained at each time step by cubic interpolation between the measurement points.Values at section mid-depth were used for each section.However, an uncertainty persisted as to the actual average depth of the topmost set of 4 tubes in the soil, which was especially significant in relative value (absolute error: 1.1 cm and relative error: 22%).Since we were considering purely diffusive transport, an accurate knowledge of this depth was particularly necessary; we therefore fitted the upper-tube average depth (around 5 cm) so that the diffusive estimated flux at the soil surface matched the F s measurements.

Profiles of air-filled porosities and soil diffusion coefficients
The total porosity of intact soil samples was determined by vacuum pycnometry (Maier et al., 2010).[10] Atmospheric pressure was supposed constant within the whole profile and equal to the value measured in the air canopy by the meteorological station.D r is a function of SWC established in undisturbed soil cores (see above).The cores were saturated with water, then successively drained to pre-defined levels of water potential (-1, -3, -6, -16 and -30 kPa in a filter bed; -90 kPa using a pressure plate).Gas diffusivity was measured at all potentials tested between −1 and −90 kPa, following a one-chamber method similar to that of Jassal et al. (2005), with neon (Ne) as a tracer gas (see Maier et al. 2010 for detailed procedure).For each depth, a specific D r (SWC) function was deduced by fitting a linear regression on all the data obtained from the samples taken at this depth.The D r value for each sections in FGA was determined by introducing the SWC value of this section into one D r (SWC) function according to the depth of the section.
The effective diffusion coefficients at the boundary between two 5-cm-thick sections, used in Eq (3) and Eq. ( 4) were calculated as the harmonic average Ds on both sides (+/-2.5 cm) of the section boundary.

Computation and analysis
Production of CO 2 , 12 CO 2 and 13 CO 2 was calculated in each 5-cm section using an FGA script (Goffin et al., 2014) on Matlab (R2014a version) and summed for each layer: layers 1 and 2 included two 5-cm-thick soil sections, while layer 3 included 4 sections.
We focused our analyses on four periods for which the fluxes, profiles and auxiliary data were all continuously available.
These periods were spread over the whole 2014 growing season and presented contrasted climatic conditions and dynamics (Table 1).
The response of [11] where SWC fc is the soil water content at field capacity (determined from laboratory measurements) and SWC min the minimal measured soil water content.The coefficient a (µmol m -2 s -1 , representing P_CO 2 or F s standardized at 0°C and SWC fc ), and the temperature coefficient Q 10 (gauging P_CO 2 or F S sensitivity to temperature) were adjusted during the fit.

P_CO 2 and δ 13 P_CO 2 vertical profiles and their seasonal changes
Over the four selected time periods, average P_CO 2 in the third soil layer was two to three times lower than in the upper layers (Fig. 2); at least 89% of the total soil production was confined to the upper 20 cm of soil whatever the period (Fig. 3).
Moreover, 64 to 77% of the CO 2 was produced in the second layer during spring while the partitioning between layers 1 and 2 was more balanced during summer, with 36 to 39 % in layer 1 and 50 to 53% in layer 2.
Excluding a few values in layers 1 and 3 which correspond to a particularly dry period in June 2011 or to very low flux periods, the isotopic composition of CO 2 production ranged from -30.4 ‰ to -17.5 ‰ in the first layer, from -30.3 ‰ to -26 ‰ in the second layer and from -32.6 ‰ to -22.4 ‰ in the third layer (Fig. 2).During April, δ 13 P_CO 2 in the first layer was strongly enriched (δ 13 P_CO 2,1 = -23.4‰ on average) compared to δ 13 P in the second layer (δ 13 P_CO 2,2 = -27.8‰ on average) and compared to δ 13 P_CO 2,1 during August (δ 13 P_CO 2,1 = -25.9‰).The vertical profile for δ 13 P_CO 2 was gentler in July and August with a δ 13 P_CO 2,2 of -28.5 ‰ on average; in other words, relatively similar to the profile for April.
δ 13 P_CO 2 was more variable in layer 3 than in the other two layers, but these fluctuations were unreliable.

P short-term temporal variability
From April 21 st to 27 th , a sunny period with no rain (Fig. 4b and Fig. 4c), P_CO 2 showed pronounced and regular within-day fluctuations in the first and second layers (maximum difference of 0.83 ± 0.32 (SD) µmol m -2 s -1 and 1.08 ± 0.40 (SD) µmol m -2 s -1 respectively between the daily max.and min.on average over the period, Fig. 4e).P_CO 2 was more stable in the third layer (0.19 ± 0.04 (SD) µmol m -2 s -1 ).Soil temperature also showed regular fluctuations but within a narrow range (maximum difference of 0.8 ± 0.2 (SD) °C in layer 1 and 0.5 ± 0.1 (SD) °C in layer 2 between the daily max.and min.on average over the period, Fig. 4d).
In addition to within-day fluctuations, pronounced day-to-day variations in P_CO 2 were observed, for example from August 3 rd to 21 st , a period with multiple rain events.Interestingly, a drop in P_CO 2,2 was related to a drop in soil temperature and respectively, whereas minimum P_CO 2,2 was not observed until DOY 224.It is particularly notable that P_CO 2,1 (decrease from 7.1 µmol m -2 s -1 on DOY 221 to 1.9 µmol m -2 s -1 on DOY 224) and δ 13 P_CO 2,1 (enrichment from -27.7 ‰ to -21.7 ‰ between the same dates, Fig. 4k and Fig. 4l) showed an opposite trend.

Temperature sensitivity of CO 2 production
On the overall data set combining the half-hour values for the four study periods, we used an exponential function of T multiplied by a linear function varying from 1 to 0 when SWC declined (equation 11) to test P_CO 2 dependence on T and SWC.
Production in each of layers 1 and 2 was best explained with dependence on the temperature and soil water content measured within that layer compared to dependence on variables measured within another layer.For the third layer, production levels were too weak and presented such narrow fluctuations that it was impossible to fit any satisfactory equation.Exponential fits of P_CO 2 against temperature without taking SWC into account generated unrealistic Q 10 values (> 10), probably because of the narrow range of investigated temperatures (10.8°C to 18.2°C at 5 cm depth over the season) and the covariance of T with other factors influencing P_CO 2 processes.When SWC was included in the equation, more realistic Q 10 values were obtained (Table 2) and the value determined for F S standardized at 0°C when soil water content is at field capacity, was roughly the sum of the P_CO 2 obtained for the first and the second layer under the same conditions (Table 2, parameter a in Eqn.11).The Q 10 of P_CO 2 was significantly higher in the second layer compared to the first layer, and to the Q 10 of F S .

Temporal variability of δ 13 P_CO 2
Throughout the whole dataset, the distribution of δ 13 F s was shifted towards more positive values compared to δ 13 F t (Fig. 5a).

Relationship between soil production and canopy activity
The second layer was the largest contributor to total soil production (more than 50% of the total emitted CO 2 ).Furthermore, different anomalies were identified for δ 13 P_CO 2 in the first layer (non-reliable variability due to atmospheric pollution, see section 4.2.) and in the third layer (low P_CO 2,3 intensity leading to indeterminate or beyond-range values, see section 4.2.).
Daily average δ 13 P_CO 2,2 was correlated with the previous day's gross primary production (GPP, R=0.51), evapotranspiration (ET, R=0.45), and even more closely with inherent water use efficiency (IWUE, R=0.67, Fig. 7).A simple multivariate linear regression with the IWUE of the previous day and the SWC of the current day explained 76% of the dayto-day variation in δ 13 P_CO 2,2 (Fig. 6b).

The production of CO 2 and its vertical profile
The production values we found are in agreement with the soil CO 2 effluxes already published for this site (Epron et al., 1999;Ngao et al., 2012), except for values in June 2011 when P_CO 2 determined with FGA resulted in a few incoherent negative values in the first and third layers (Fig. 2b).For the first layer, this may have been due to the rather dry period that occurred at that time (Table 1); large air-filled porosity may have favored transport through the top soil via processes other than diffusion (advection and dispersion) (Bowling and Massman, 2011;Flechard et al., 2007;Risk et al., 2008).This situation could have caused atmospheric and soil air to mix in the first centimeters, thus leading to a very low (even inverted) vertical gradient in CO 2 concentrations.Under such conditions, fluxes computed with FGA (where only diffusion transport is considered) could be underestimated and even negative.Negative production values in the third layer occurred when the concentration gradient was within the measurement uncertainties of the analyzer.
The vertical P_CO 2 profile calculated with FGA showed that 90 % of CO 2 production occurs in the two first layers (Fig. 3), in agreement with Goffin et al. (2014) and Jassal et al. (2005) who showed that 75% of the soil CO 2 efflux comes from the top 20 cm in two other temperate forests.This is consistent with the vertical distribution of roots and soil organic matter (SOM); more than 65% of the roots and 73% of SOM are located in the upper 20 cm (Fig. 1).The low contribution of the third layer to total soil P_CO 2 can be explained by a lower root biomass (less than one third of the root biomass was in this layer) and by stronger physical protection of SOM from microbial attack since the deep soil was composed of more than 30% clay (Baldock and Skjemstad, 2000;Lützow et al., 2006).
Temperature has been recognized as the main environmental driver of seasonal variations in soil CO 2 efflux in temperate ecosystems (Davidson et al., 2006a;Kätterer et al., 1998;Raich et al., 2002).In this study, when both temperature (T) and soil water content (SWC) were combined together in a single empirical equation, variations in CO 2 production could be satisfactorily simulated (Table 2) when fitted over the four study periods from spring to summer.The computed Q 10 values were high (3.3 and 5.3), higher than those expected for root and microbial respiration (2 to 3, Jenkins and Adams, 2011;Lloyd and Taylor, 1994;Ryan et al., 1996;Zogg et al., 1996) but remained within the range of published values for soil CO 2 efflux in temperate forests (Borken et al., 2002;Davidson et al., 1998;Epron et al., 1999;Janssens and Pilegaard, 2003).
Previously, high Q 10 values observed for soil CO 2 efflux have often been blamed on a mismatch between the depth where soil temperature is measured and the depth where CO 2 production occurs.Indeed, when temperature is measured below CO 2 production, and because the seasonal range of soil temperature decreases with depth (Hirano et al., 2003;Pavelka et al., Biogeosciences Discuss., doi:10.5194/bg-2016-194, 2016 Manuscript under review for journal Biogeosciences Published: 17 May 2016 c Author(s) 2016.CC-BY 3.0 License.

2007
), an overestimation of temperature sensitivity (Q 10 ) is needed to reproduce P_CO 2 variability.In our study, the Q 10 of the soil CO 2 efflux matched the expected intrinsic value (2.2), even though high Q 10 (5.3) values were calculated for the second layer and, to a lesser extent, for the first layer (Q 10 = 3.3).Because we used the temperature measured in the same layer where CO 2 production was computed, the high Q 10 values cannot be related to a mismatch between P_CO 2 source and measurement depth.These high values are therefore most likely due to the confounding effects of T with other abiotic drivers (PPFD) or/and to changes in basal activity of either the autotrophic or heterotrophic source at a seasonal scale (Epron et al. 2000).For example, root growth peaks in late spring and early summer, and C allocation to soil CO 2 efflux varies seasonally and peaks in July (demonstrated by pulse labeling tree photosynthesis with 13 C, Epron et al. 2011).
At shorter time scales (within-day, day-to-day), the variation in soil temperature was too narrow to account for variations in production.In addition, the lag between the decrease in temperature and the decrease in production, as seen in August (Fig. 4j and Fig. 4k), suggests that temperature is not the main driver of day-to-day variations in CO 2 production.The next section provides information about potential factors affecting these variations.

Isotope composition of CO 2 production
The isotopic composition of CO 2 produced throughout the season we estimated was within the range reported in the literature (Bowling et al., 2008;Goffin et al., 2014).The CO 2 produced in the first layer (δ 13 P_CO 2,1 ) was more enriched than the soil CO 2 efflux (δ 13 F S ), while the CO 2 produced in the second and third layers (δ 13 P_CO 2,2 or δ 13 P_CO 2,3 ) was more depleted (Fig. 5).While the opposite trend for P_CO 2,1 and δ 13 P_CO 2,1 may attest to the presence of a depleted source that increasingly supplies layer-1 production, it is more likely that δ 13 P_CO 2,1 and P_CO 2,1 were simultaneously and respectively over-and underestimated when upper soil CO 2 was mixed with atmospheric air during turbulence events.Effectively, any input of atmospheric CO 2 by advection or dispersion (with lower concentrations and higher δ 13 ) would generate artifacts on P_CO 2 and δ 13 P_CO 2 estimations because only diffusion is considered in FGA (Kayler et al., 2010).Mixing soil and atmospheric air could also explain the enrichment of δ 13 P_CO 2,1 compared to δ 13 F S, and the fact that, while the distribution of δ 13 P_CO 2,2 and δ 13 P_CO 2,3 was normal, the distribution of δ 13 P_CO 2,1 formed a lognormal shape.Finally, a few values computed for the third layer were beyond the expected range, which could result from the greater uncertainties when calculating the ratio of 13 C to 12 C production when values are close to 0.
The isotopic composition of the CO 2 produced in the second soil layer (δ 13 P_CO 2,2 ) was close to the isotopic composition of tree trunk CO 2 efflux (δ 13 F t ).The similarity between δ 13 P_CO 2,2 and δ 13 F t distributions suggests that autotrophic activity largely contributes to CO 2 production in this second layer.This layer contained the same amount of roots as the two other layers, but probably a lower amount of labile organic matter than the first layer (Braakhekke et al., 2011;Rumpel et al., 2002).At the daily time scale, δ 13 P_CO 2,2 was well correlated with the IWUE measured the day before (Fig. 7); this attests to a link between canopy activity and soil autotrophic production in the second layer.Indeed, the connection between the dayto-day fluctuations in δ 13 P_CO 2,2 and canopy activity is related to fractionation occurring during photosynthesis, carbohydrate transport and respiration (Griffis, 2013).Carbon isotope discrimination during photosynthesis depends on the  Farquhar et al. 1982) and impacts the δ 13 C of the photosynthetic products that fuel respiration (Ekblad and Högberg, 2001;Gessler et al., 2007).The fluctuations in δ 13 P_CO 2,2 we found therefore reflect temporal climate-driven variations in photosynthetic carbon isotope discrimination, and the one-day delay of δ 13 P_CO 2,2 response to IWUE is coherent with the time necessary for the photosynthates to be transported belowground.Pulse labeling trees with 13 C has revealed a lag between tree crown assimilation and soil CO 2 efflux of about 0.5 -1.5 days for the Hesse site (Plain et al. 2009;Epron et al. 2011).This is also consistent with the lagged decline in P_CO 2,2 after a decrease in photon flux density in August (Fig. 4i: DOY 219 and Fig. 4k: DOY 221).Moreover, P_CO 2,2 and δ 13 P_CO 2,2 were strongly correlated in our study, with enrichment occurring when production increased (Fig. 6).One explanation is that a temporal increase in gross primary production may stimulate root and rhizospheric respiration with a 24h delay, and that high rates of leaf CO 2 assimilation accounting for the increase in GPP decreases intercellular carbon dioxide concentrations in the leaves, thus decreasing carbon isotope discrimination during photosynthesis (Seibt et al., 2008).Furthermore, we performed a simple multivariate linear regression between δ 13 P_CO 2,2, the IWUE of the previous day and the SWC of the current day which suggests that, in addition to an autotrophic source related to lag variations in IWUE, a source responsive to short-term changes in soil water content contributes to CO 2 production in the second layer.Microbial respiration is highly sensitive to local changes in SWC (Moyano et al., 2012;Orchard and Cook, 1983) and is thought to respond faster to fluctuation in SWC than root respiration.We therefore hypothesize that heterotrophic sources also contribute to CO 2 production in the second soil layer, though our data did not allow us to quantify the relative contribution of autotrophic and heterotrophic sources to CO 2 production.

Conclusion
The combination of FGA with high frequency measurements of soil CO 2 isotopic composition allowed us to determine the vertical distribution of CO 2 production (P_CO 2 ) and its isotopic composition (δ 13 P_CO 2 ), especially during calm weather periods with low atmospheric turbulence.Most CO 2 production (90 %) occurred in the upper 20 cm of the soil and was related to root and SOM vertical distributions.The P_CO 2 seasonal variability of each layer was best related to its own temperature, with significant differences in temperature sensitivities among the layers.Significant day-to-day fluctuations were observed for P_CO 2 and δ 13 P_CO 2 , especially in the second layer, but the variation in soil temperatures was too narrow to account for these variations.However, these fluctuations seems to be due to a large contribution from autotrophic sources, since a strong link between P_CO 2 , δ 13 P_CO 2 and canopy activity (through inherent water use efficiency) was found for the second layer.In addition, heterotrophic sources responding to rapid changes in soil water content also contributed to CO 2 production in this layer.We were not able to separate the contribution of autotrophic and heterotrophic sources to CO 2 production because of their temporal variability and because the differences in their isotopic signatures were too small.Despite this limitation, the isotopic flux-gradient approach gave consistent and promising results.Production estimates in the top soil layers will be further improved in the future by accounting for turbulent advection and dispersion processes.
Table 1: Minimum, maximum and average soil temperature (T) and soil water content (SWC) measured at 5 cm depth, average gross primary production (GPP) and evapotranspiration (GPP) and cumulated rain over of the four selected time periods.
Four undisturbed soil cores (200 cm 3 , 5 cm in height) were extracted at 0-5, 10-15, 20-25 and 40-45 cm depth.Air-filled porosity ( ) was obtained from the difference between total porosity and volumetric water content.One value was assigned to each section in FGA according to the depth of the section.The effective soil diffusion coefficient (Ds) was estimated every centimeter as a function of the free air CO 2 diffusion coefficient in standard conditions (D 0 = 1.47×10 −5 m 2 s −1 at 293.15 K and 101.3 Pa), atmospheric pressure (Pa,[Pa]), temperature at the corresponding depth (T [K]) and the relative soil diffusion coefficient (D r = D s /D 0 defined as the tortuosity factor) followingCampbell (1985): F S and P_CO 2 to temperature was evaluated on Matlab (R2014a version) by fitting a combined Q 10 temperature function and water content function varying from 0 at minimum SWC to 1 at field capacity (already successfully used for this site by Epron et al. (1999): Biogeosciences Discuss., doi:10.5194/bg-2016-194,2016 Manuscript under review for journal Biogeosciences Published: 17 May 2016 c Author(s) 2016.CC-BY 3.0 License.
content at either 5 cm depth (P_CO 2,1 ) or at 15 cm depth (P_CO 2,2 and F S ).The retained depths for soil temperature and water content were those giving the highest coefficients of determination (R 2 ).Parameter 'a' is F S or P_CO 2 standardized at 0°C when soil water content is at field capacity.Q 10 is the temperature sensitivity.a (µmol m

Figure 1 :
Figure 1: Vertical distribution of average total porosity (m 3 m -3 , the error bars correspond to the standard deviation between samples), fine root proportion (% of total root content over the profile), soil water content at wilting point (SWC wp , m 3 m -3 ), soil water content at field capacity (SWC fc , m 3 m -3 ) and SOM content in the three defined layers [1] 0 to -10 cm, [2] -10 cm to -20 cm 570

Figure 3 :
Figure 3: Average contribution of each layer to total soil CO 2 production for the four different time periods (a) 21 to 27 April, (b) 580

Figure 6 :
Figure 6: Relation (a) between day-to-day variation in daily means of δ 13 P_CO 2,2 during August (03/08 to 21/08) and day-to-day variation in daily means of P_CO 2,2 , and (b) between daily means of observed δ 13 P_CO 2,2 and predicted δ 13 P_CO 2,2 using a multivariate linear regression against SWC measured at 15 cm on the same day and IWUE measured the previous day.

Figure 7 :
Figure 7: Upper panels: Correlation coefficients between daily means of δ 13 P_CO 2,2 and gross primary production (GPP, left), evapotranspiration (ET, middle) and inherent canopy water use efficiency (IWUE, right) with a lag ranging from 0 to 4 days.Maximum correlations are identified by black diamonds and the corresponding linear regression is plotted below.