2.1 Site description and experimental set-up

The experiment was conducted in a managed pure 130-year-old beech stand at ~100 m distance to the Fluxnet tower site Leinefelde (DE-Lnf, https://doi.org/10.18140/FLX/1440150) in the forest district of Heiligenstadt near the city of Leinefelde (51°20′N, 10°22′E; altitude 450 m a.s.l; Thuringia; central Germany). The mean annual air temperature and precipitation are 8.3 ± 0.7°C and 601 ± 154 mm (Tamrakar et al., 2018). We measured four even-sized mature beech trees with a tree height of ca. 38 m and stem diameter at breast height (DBH) ranging between 0.38 and 0.54 m (Table 1) during July and August 2019 (Days of year [DOY] 185–226).

2.2 Stem CO₂ efflux, O₂ influx and xylem [CO₂]

The concentration of xylem [CO₂] in the gas phase (%) was measured with NDIR CO₂ sensors (GMP221 and GMP251; Vaisala Inc.) calibrated before installation using reference gases at known [CO₂] of 0%, 5%, 10% and 15%. For each sensor, we drilled a 40 mm deep and 25 mm wide hole into the stem and pushed the probe (length: 96 mm) halfway within the hole (~20 mm), leaving a closed headspace in the xylem tissues beyond the cambium layer. Synthetic rubber sealant (Teroson RB IX; Henkel) was used for isolation from the atmospheric gas. Four sensors were installed in each tree along the vertical profile monitored with stem chambers at 1, 2.35, 2.65 and 4 m. We initially envisaged applying the mass balance approach in the 30-cm-length stem segment between 2.35 and 2.65 m probes. Nevertheless, we eventually decided to average the xylem [CO₂] time series from these two probes to survey longer (and more representative) stem segments, from 1 to 2.5 m (lower stem) and from 2.5 to 4 m (upper stem) (Supporting Information: Figure S1). Probes were placed ca. 10 cm from each chamber on the northwest side of the trees. Readings of the 16 sensors were recorded every 5 min with a datalogger (CR1000x; Campbell Scientific) for the whole experiment period.

2.3 Xylem CO₂ transport and storage

The amount of CO₂ transported upwards through the xylem and stored within the xylem was estimated in the lower and upper stem segments. The concentration of dissolved CO₂ in xylem sap ([CO₂*], mol CO₂ l⁻¹) was calculated using temperature-dependent Henry's Law coefficients (Levy et al., 1999; McGuire & Teskey, 2002), assuming equilibrium between CO₂ in the gaseous and liquid phases. For this, xylem [CO₂] in the gas phase, xylem sap pH, and stem temperature must be known. To monitor sap pH, xylem sap was collected from twigs of low branches of monitored trees (n = 3, as one tree was inaccessible for sampling) using a Scholander pressure chamber at four sampling dates (DOYs 204, 212, 218 and 226). Sap samples were quickly placed in Eppendorf tubes and a cold box for transportation to the laboratory and then stored in a refrigerator until measurement. Xylem sap pH was measured using a pH meter (Five Easy; Mettler Toledo) with a microelectrode (InLab®, Ultra-Micro-ISM; Mettler Toledo). Preliminary tests confirmed that sap pH did not significantly vary over the sample storage period. Stem temperature (T_stem,°C) was continuously measured and recorded with a datalogger (CR1000x; Campbell Scientific) every 5 min using thermocouples inserted at 2 cm depth next to each stem chamber.

A staining method was applied to determine the sapwood area; upon extraction of one wood core per tree at breast height on the northwest side of the tree (until the pith), a blue dye (E131) was injected into the hole, and a second core was extracted one cm above the first one after 1 h. Sapwood depth was determined by the length of the stained region of the core and assuming a cylindrical shape for both heartwood and sapwood (Table 1) (Goldstein et al., 1998).

2.4 Soil water content and shoot water potential

Soil water content (%) was continuously measured at the meteorological flux tower with one sensor (ML-2x; DeltaT) inserted at 16 cm depth, 100 m away from our instrumented trees, with a temporal resolution of 10 min. Shoot water potential (MPa) was measured around solar midday (as for sap pH sampling) at four sampling dates (DOYs 204, 212, 218, and 226) using the Scholander pressure chamber.

2.5 PEPC capacity and NSC in woody tissues

We took one stem disc (one cm-length, bark to xylem) at three stem heights (1, 2.5, and 4 m) on the south side of each monitored tree on 14 August (DOY 226). Samples were immediately frozen in liquid nitrogen to stop the metabolic activity and transported to the laboratory. Stem discs were stored at −80°C before grinding into a fine powder in liquid nitrogen with a mortar and pestle. 20 mg of woody tissue material was used for the discontinuous assay performed in a 96-well microplate (Bénard & Gibon, 2016). Briefly, aliquots were extracted by shaking with an extraction buffer. After centrifugation (7 min, 3000 g, 4°C), extracts were diluted and incubated for 20 min. The reaction was stopped with HCl. The sealed microplate was then incubated at 95°C for 10 min to destroy NADH. After cooling down, each well was neutralised with NaOH and Tricine-KOH pH 9.0 to adjust the pH to 9.0. The absorbance was read at 570 nm (30°C) until rates were stabilised. Reaction rates (mOD min⁻¹) were used to calculate the amount of NAD⁺ formed during the first step of the assay. All pipetting steps were performed using a 96-head robot (Hamilton Star), and absorbances were measured in a filter-based microplate reader (SAFAS MP96). For further details, see Supporting Information: Methods S1 and Bénard and Gibon (2016).

We measured soluble sugars and starch in stem cores from the instrumented trees following the Landhausser et al. (2018) protocol. One stem core per height (1, 2.5, 4 m, south-side) was collected on 4 July (DOY 185) and 14 August (DOY 226) for NSC measurements. Samples were stored in cooling bags for transportation and then oven-dried at 60°C for 72 h. Stem cores were cut into two 2-cm long sections starting at the cambium (wood depth: 0–2 cm and 2–4 cm) and ground into a fine powder (ball mill, MM 400; Retsch). We extracted the soluble sugars glucose, fructose, sucrose, and starch from each sample. Briefly, ~30 mg of dry plant powder was extracted with 80% ethanol. Supernatants were analysed by High-Performance Liquid Chromatography coupled to a Pulsed Amperometric Detection (HPLC-PAD) for soluble sugar determination. We enzymatically converted the starch from the remaining pellet to glucose using α-amylase amyloglucosidase. Glucose hydrolysate was measured by the HPLC.

2.6 Data analysis

Statistical analyses were performed using R software (R Development Core Team, 2019). CO₂ efflux and O₂ influx data were discarded when the R² of the linear fit for CO₂ and O₂ readings were below 0.96 to ensure good data quality. For gap filling, we used the pad function in padr package. To test whether the average daily values of CO₂ efflux, O₂ influx and xylem [CO₂] varied with stem height, linear mixed models were adjusted using the lme function in nlme package (Pinheiro et al., 2017), considering height as a fixed factor and tree as a random factor including an autocorrelation structure to account for repeated measurements. To test whether PEPC capacity varied with stem height, and sap pH among sampling dates, linear mixed models were adjusted likewise, considering the tree as a random factor. The normality of residuals was checked visually. When significant, differences among heights were tested post hoc with Tukey contrasts using the emmeans function (emmeans package). Consistency between carbon- and oxygen-based measurements was tested by evaluating the relationship between R_S (E_CO2 + F_T + ΔS) and O₂ influx, and between CO₂ internal fluxes (F_T + ΔS) and ARD, with mixed models considering tree a random factor. Potential deviances from the 1:1 relationship would indicate a lack of consistency between methodological approaches, hence the need to revisit the underlying assumptions of Equation (3). The conditional and marginal R² (Nakagawa & Schielzeth, 2013) of these models was estimated using r2_nakagawa function (performance package) to further evaluate the degree of agreement between approaches. Finally, sap flow, sap [CO₂*] and the ARD were normalized to their daily maxima, and subdaily patterns were compared to evaluate the potential of xylem transport to remove locally respired CO₂ on a subdaily basis.

3.1 Stem temperature, soil water content, sap flow rate and shoot water potential

The mean stem temperature during the experiment was 17.7°C, with minimum values of 10°C during early July and peaking at the end of July with values close to 30°C (Figure 1a). Volumetric soil water content at 16 cm depth was lowest end of July, reaching minimum values of 15.7 vol% and maximum values of 19.0 vol% afterwards following summer rains (Figure 1b). Sap flow rate showed a typical subdaily pattern with maximum rates of 30 l h⁻¹ during sunny and warm days (Figure 1c). Shoot midday Ψ (shoot water potential) was close to −1.4 MPa on most measurement days, except the one following rains when it relaxed up to −0.5 MPa (Figure 1c).

3.2 Gas exchange and internal [CO₂] at different stem heights

The vertical position did not affect CO₂ efflux and O₂ influx (p = 0.69 and 0.71, respectively). Mean daily CO₂ efflux (±SE) was 2.9 ± 0.6, 2.7 ± 0.4 and 2.3 ± 0.6 μmol m⁻² s⁻¹ at 1, 2.5, and 4 m stem height, respectively (Figure 2a). Mean daily O₂ influx was 4.1 ± 0.7, 3.9 ± 0.5 and 3.3 ± 0.6 μmol m⁻² s⁻¹, respectively (Figure 2b). O₂ influx was consistently higher than CO₂ efflux along the vertical gradient (p < 0.001), resulting in mean daily ARQ of 0.71 ± 0.04, 0.69 ± 0.04 and 0.69 ± 0.06 at 1, 2.5 and 4 m stem height, respectively (Figure 2c). Xylem [CO₂] ranged from ca. 5.9% to 12.4%, with no significant effect of height over the whole surveyed period (Figure 2d; p = 0.11). However, when considering the last third of the experiment (1–14 August), stem height did affect xylem [CO₂] (p = 0.03), with values being lower at 1 m compared with 2.5 m height. Sap pH ranged between 6.48 and 7.41 over the measurement period (Figure 2d), and differences in sap pH among trees (p = 0.17) or dates (p = 0.21) were not significant. Stem temperature had a strong effect on xylem [CO₂] (p < 0.001), CO₂ efflux and O₂ influx (p < 0.01). Likewise, respiratory fluxes had maximum values during the afternoon, following subdaily thermal dynamics.

3.3 PEPC capacity and NSC at different stem heights

Stem height had no significant effect on PEPC capacity in the outermost stem section (p = 0.23) and did not differ among trees (p = 0.93). Mean PEPC capacity was 760.5 ± 201.6, 661.25 ± 60.2 and 547.25 ± 77.4 nmol min⁻¹ gFW⁻¹ at 1, 2.5 and 4 m, respectively.

Stem height did not affect soluble sugar and starch concentrations (p = 0.37 and 0.40, respectively) (Figure 3). Sapwood depth did affect NSC; both soluble sugar and starch concentrations were higher near the cambium (0–2 cm) than deeper into the sapwood (2–4 cm) (p < 0.05). Soluble sugar and starch concentrations were higher on the second sampling date in August (DOY 226) for the 0–2 cm depth (p < 0.001, p < 0.01 for soluble sugar and starch, respectively), while they remained constant deeper into the cambium (p = 0.1, p = 0.6 for soluble sugar and starch, respectively).

3.4 Comparison of carbon- and oxygen-based estimates of R_S

We applied the mass balance approach on the lower (1–2.5 m) and upper (2.5–4 m) stem segments to estimate R_S and its contributors for comparison with the oxygen-based approach (Figure 4). In the lower stem segment, there was a positive vertical gradient in sap [CO₂*], and CO₂ transport was, therefore, positive. Averaged across days and trees, the contribution of CO₂ efflux to R_S was 64.6 ± 14.5%, and the remaining fraction was attributed to CO₂ transport (35.8 ± 14.3%), as CO₂ storage was negligible (−0.4 ± 0.2%). The R_S daily average (as the sum of E_CO2, F_T and ΔS) was greater than O₂ influx, but on a subdaily basis, R_S exceeded O₂ influx only during the daytime. During night-time, R_S equalled CO₂ efflux, and both were lower than O₂ influx.

The upper stem showed a different pattern where the vertical gradient in sap [CO₂*] approached zero and even became negative for the last 2 weeks of our study. As a consequence, the relative contributions of CO₂ transport (−1.2 ± 2.2%) and CO₂ storage (0.0 ± 2.2%) to R_S were negligible, and apparently, all the respired CO₂ diffused to the atmosphere (E_CO2 = 101.1 ± 22.9%). In this stem section, both CO₂ efflux and R_S were on average lower than O₂ influx for most of the surveyed period. Notably, the shift from positive towards negative CO₂ transport flux followed the peak in temperature and transpiration at the end of July.

Daily values of stem CO₂ efflux and O₂ influx showed good agreement (Figure 5a) with a slope of 0.65 ± 0.02 (p < 0.0001), a significant intercept of 0.23 ± 0.11 (p < 0.05), and conditional and marginal R² of 0.87 and 0.86, respectively. When this relation was forced through the origin (the intercept is zero), the slope increased to 0.69 ± 0.02, which is in better agreement with the mean ARQ of 0.70. Nevertheless, carbon- and oxygen-based estimates of R_S showed poor consistency. Although R_S and O₂ influx were positively related (Figure 5b), the deviation of the mean slope from unity was significant (1.57 ± 0.18; p < 0.0001), as well as its intercept (−2.08 ± 1.01; p < 0.05). The model conditional and marginal R² were 0.52 and 0.31, respectively. The slope of the relation between the ARD and CO₂ internal fluxes (F_T + ΔS) (Figure 5c) was almost 0 (0.056 ± 0.012; p < 0.0001), and its intercept was again significant (0.84 ± 0.09; p < 0.0001), denoting the limited potential of CO₂ transport and storage to bridge the gap between CO₂ efflux and O₂ influx. The conditional and marginal R² of this model were 0.21 and 0.13, respectively. Stem location did not affect the intercept of any of these relations (p > 0.1), according to the lack of consistency in vertical gradients of respiratory-related variables.

To further evaluate the potential of the transpiration stream to transport respired CO₂ away from its point of production, we evaluate the subdaily patterns of ARD, sap flow and sap [CO₂*] (as a proxy of CO₂ solubility). For the comparison, we normalized the values of each variable to their corresponding daily maxima (Figure 6). Compared with sap flow dynamics, the ARD showed a relatively stable pattern over the 24-h period. It was higher during the daytime, with night-time reductions of ca. 30%–35% relative to the daily maxima. By contrast, sap flow showed night-time reductions of ca. 85%–90% relative to the daily maxima, denoting subdaily decoupling between CO₂ transport and the ARD. Subdaily variation in sap [CO₂*] was minimal, with the highest values observed during night-time and limited reductions during daytime (<2%) according to the inverse relation between solubility and temperature.

4.1 CO₂ internal fluxes cannot explain the differences between stem O₂ influx and CO₂ efflux

Higher O₂ influx than CO₂ efflux could result from the higher solubility of CO₂ in xylem sap (30 fold) compared with O₂ (Dejours, 1981), hence the possibility of CO₂ dissolving in the sap solution and being transported upwards or stored. If true, this would be evident in our mature beech trees, whose large sapwood conducting area provides room for potentially high transport and storage of respired CO₂ (Fan et al., 2017). We found a nonneglectable contribution of CO₂ transport to R_S, up to 1/3 in the lower stem segment, highlighting the potentially significant role of CO₂ xylem transport in diverting root-respired CO₂ from soil measurements (Aubrey & Teskey, 2021). Nevertheless, we found two lines of evidence refuting our hypothesis, as CO₂ internal fluxes could not bridge the gap between stem O₂ influx and CO₂ efflux. First, the relation between O₂ influx and R_S diverged from the 1:1 line (Figure 5b), as indicated by a slope different from the unit and a significant intercept. Furthermore, the marginal R² = 0.31 of this relation denotes that stem O₂ influx accounted for less than one-third of the variability in the carbon-based estimate of R_S. Identical reasoning applies to the comparison between CO₂ internal fluxes (F_T + ΔS) and ARD (Figure 5c), with a marginal R² of 0.13, further supporting the limited potential of xylem CO₂ transport and storage to predict the ARD. Second, if the ARD could be primarily ascribed to xylem CO₂ transport, ARD and sap flow subdaily variability should follow similar patterns (Bowman et al., 2005; McGuire & Teskey, 2004; McGuire et al., 2007). However, the subdaily variation in ARD was limited compared with sap flow (Figure 6). Specifically, ARD maintained values above 50% of the daily maxima during night-time, when sap flow was reduced to a much larger extent, down to 10%–15% of the daily maxima. Moreover, sap [CO₂*] on a subdaily basis was remarkably stable, with minimal reductions during daytime ascribed to temperature-driven reductions in CO₂ solubility, partly offset by the daytime increase in respiratory activity and xylem [CO₂]. Therefore, CO₂ solubility in sap could not significantly affect the strength of CO₂ transport as a mechanism to remove respired CO₂ from its production site. Taken together, subdaily patterns of ARD, sap flow and sap [CO₂*] thus provide further evidence of the limited role of the transpiration stream in filling the gap between CO₂ efflux and O₂ influx in this study. This observation agrees with Hilman et al. (2019), showing the inability of sap flow to account for the variability in ARD of Q. ilex trees.

Nevertheless, we must be cautious about the specific methodological issues related to the measurement of sap flow and sap pH and their corresponding propagation errors. For instance, sap flow measured with the heat pulse method often underestimates the actual sap flow, on average, by 35% (Steppe et al., 2010). Considering a proportional underestimation of CO₂ transport, its contribution to R_S would also increase in parallel, affecting the difference between R_S and O₂ influx differently among individuals and heights. Sap pH, especially above 6.5, is another critical factor for calculating CO₂ transport, as the solubility of CO₂ increases exponentially with pH. Here, we applied a constant pH value across daily and subdaily temporal scales and assumed similar pH between twig sap and stem sap. However, these assumptions can lead to further CO₂ transport misestimation (Aubrey et al., 2011; Erda et al., 2014; R. Salomón et al., 2016) and deviances between carbon-based estimates of R_S and O₂ influx. Moreover, if parenchyma cells were damaged upon sap extraction, the sample might be contaminated, resulting in an overestimation of the pH values (Tarvainen et al., 2023) and hence CO₂ transport. Another source of uncertainty in ARQ estimation is the relative humidity correction applied to estimate O₂ influx. The relative humidity sensor integrated into the [CO₂] sensor has a slow response time, as shown in Helm et al. (2021). Assuming an underestimation of humidity levels in the measurement chamber by, for example, 5%, the dilution correction required for O₂ estimation would increase the ARQ by ~0.001.

Regardless of these potential measurement uncertainties, we did not succeed in reconciling differences between the two approaches, which highlights a crucial methodological difference. The carbon-based approach estimates R_S based on fluxes measured at the stem surface and internal fluxes measured in the xylem, while the oxygen-based approach relies on O₂ influx at the stem surface. Therefore, the disagreement between approaches might be related to the fact that (i) CO₂ efflux and O₂ influx likely reflect respiration in the outermost tissues of the stem (bark, phloem, cambium and outer xylem) and that (ii) respiration of the inner sapwood in large trees cannot be appropriately detected by measurements taken at the surface. According to Fick's law of diffusion, the rate of gas (CO₂ or O₂) diffusion is inversely related to the length of the diffusive pathway (Nobel, 2009) and, therefore, such decoupling likely increases in large-sized trees. Here, in the mature beech trees with a sapwood depth between 12 and 16.5 cm, the diffusion of respired CO₂ by inner living cells is much lower than in seedlings and saplings, wherein each respiring cell is located nearer to the bark-atmosphere interface. Decoupling between internal respiratory fluxes and fluxes from the stem surface can be exacerbated by the high water content of the cambium layer (De Schepper et al., 2012), acting as a major diffusion barrier according to the slow gas diffusivity in water (ca. 10⁴ times lower than in air; Nobel 2009).

4.2 PEPC-mediated CO₂ fixation as a relevant driver of the systematic mismatch between CO₂ efflux and O₂ influx

Higher O₂ influx than CO₂ efflux could be explained by CO₂ refixation via PEPC, which hinders CO₂ from being locally emitted. We measured PEPC capacity of 656 nmol min⁻¹ g FW⁻¹, equivalent to 22 nmol s⁻¹ g DW⁻¹ (assuming stem water content of 50%). For comparison, the PEPC capacity in current-year twigs of beech trees was 13 nmol s⁻¹ g DW⁻¹ (Hilman et al., 2019, recalculated from Berveiller & Damesin 2008), and 17 nmol s⁻¹ g DW⁻¹ in Pinus sylvestris (Hilman et al., 2019, recalculated from Ivanov et al., 2006). Therefore, the capacity of CO₂ refixation via PEPC measured here was comparable with that observed in younger, greener twigs.

In nonphotosynthetic tissues, PEPC is involved in anaplerotic reactions, compensating for the depletion of C skeletons consumed by the tricarboxylic acid cycle towards other pathways (synthesis of amino acids) or even other organs (export of malate and citrate via the xylem stream). Part of the phosphoenolpyruvate (PEP) produced by glycolysis may be converted to oxaloacetate and further to malate, with a zero net balance of ATP and NADH during the fixation of two molecules of CO₂. Given the low ARQ values observed here, the resulting malate may not be locally oxidized, but further metabolized to produce, for example, citrate or amino acids. Evidence shows that malate concentration increases in the stem of Acer platanoides trees moving upwards (Schill et al., 1996). Transported malate can increase the malate pool in leaves (Gessler et al., 2009), where it could be metabolized via malic enzymes releasing CO₂, thus favouring carboxylation via Rubisco (Hibberd and Quick 2002). Alternatively, the products can be transported downwards via the phloem (Hoffland et al., 1992; Shane et al., 2004; Touraine et al., 1992), followed by excretion in the rhizosphere as root exudates. Alternatively or additionally, PEPC could be involved in pH regulation (Caburatan & Park, 2021), the latter having appeared stable despite fluctuations in xylem CO₂ (see e.g. Erda et al., 2014). Extrapolating PEPC capacity on a volume basis for comparison with CO₂ efflux or O₂ influx (as in Figure 4) resulted in unrealistically high rates of PEPC fixation (up to two orders of magnitude higher than R_S estimates). First, enzyme activity measured in vitro under saturating substrate usually exceeds the in vivo flux (Junker et al., 2007). Second, PEPC capacity likely decreases with xylem depth (Höll, 1974), and PEPC samples were uniquely taken from the outermost stem tissues. Nevertheless, the high values of PEPC capacity on a volume basis suggest that even low PEPC capacity could be significant for the stem C budget and could help explain the discrepancy between CO₂ efflux and O₂ influx.

4.3 Other potential C sinks

Another potential missing C sink in R_S budgets is the CO₂ photosynthetic refixation occurring in chloroplast-containing cells located in peripheral woody tissues (Ávila et al., 2014; De Roo et al., 2020; R. O. Teskey et al., 2008), which can reduce stem CO₂ emissions by half, as observed in young poplar trees (De Roo et al., 2020). However, local photosynthetic fixation can be safely discarded within our experimental set-up, as opaque stem chambers were used to measure CO₂ efflux, precluding photosynthetic light reactions. Nevertheless, we cannot discard the possibility of axial diffusion of CO₂ in the gas phase ascribed to distant woody tissue photosynthesis (De Roo et al., 2019; Saveyn, Steppe, & Lemeur, 2008). In this line, light-driven photosynthesis above and below the (opaque) stem chamber can develop light-induced vertical [CO₂] gradients, leading to CO₂ axial diffusion in the gas phase that has been observed to reduce CO₂ efflux by 22% in oak stems (De Roo et al., 2019). Furthermore, we cannot rule out the possibility of O₂ influx measurements overestimating stem respiratory activity. We must critically note that O₂ influx measurements should be considered as additional information that helps disentangle CO₂ sinks and sources, but not as an equivalent to R_S as uncertainties remain. First, a shift in the respiratory substrate from NSCs to lipids or proteins, with a lower oxidation state, requires a higher amount of O₂ for respiratory reduction, hence increasing the ARD (and reducing the ARQ; Fischer et al., 2015; Hanf et al., 2015). However, our study extended over 6 weeks during the summer season and measured NSC concentrations at different heights and depths did not indicate a seasonal NSC depletion that would alter the respiratory substrate (Figure 3). Moreover, beech is not known to store lipids (Hoch et al., 2003), further suggesting the limited role of substrate change on the ARD. Secondly, nonrespiratory O₂ uptake by O₂-consuming enzymes like oxidases and hydroxylases (Sweetlove et al., 2013) that are not involved in respiratory metabolism may increase O₂ influx while CO₂ efflux remains constant (Kruse & Adams, 2008; O'Leary et al., 2019; Tcherkez et al., 2012). Thirdly, high growth rates related to cell wall deposition, likely occurring at the end of the growing season, may also lead to a nonrespiratory increase in O₂ consumption, as observed in Pinus radiata (Kruse & Adams, 2008).