Diurnal variation in mesophyll conductance and its influence on modelled water-use efficiency in a mature boreal Pinus sylvestris stand

Mesophyll conductance (gm) is a critical variable for the use of stable carbon isotopes to infer photosynthetic water-use efficiency (WUE). Although gm is similar in magnitude to stomatal conductance (gs), it has been measured less often, especially under field conditions and at high temporal resolution. We mounted an isotopic CO2 analyser on a field photosynthetic gas exchange system to make continuous online measurements of gas exchange and photosynthetic 13C discrimination (Δ13C) on mature Pinus sylvestris trees. This allowed the calculation of gm, gs, net photosynthesis (Anet), and WUE. These measurements highlighted the asynchronous diurnal behaviour of gm and gs. While gs declined from around 10:00, Anet declined first after 12:00, and gm remained near its maximum until 16:00. We suggest that high gm played a role in supporting an extended Anet peak despite stomatal closure. Comparing three models to estimate WUE from ∆13C, we found that a simple model, assuming constant net fractionation during carboxylation (27‰), predicted WUE well, but only for about 75% of the day. A more comprehensive model, accounting explicitly for gm and the effects of daytime respiration and photorespiration, gave reliable estimates of WUE, even in the early morning hours when WUE was more variable. Considering constant, finite gm or gm/gs yielded similar WUE estimates on the diurnal scale, while assuming infinite gm led to overestimation of WUE. These results highlight the potential of high-resolution gm measurements to improve modelling of Anet and WUE and demonstrate that such gm data can be acquired, even under field conditions. Electronic supplementary material The online version of this article (10.1007/s11120-019-00645-6) contains supplementary material, which is available to authorized users.


Introduction
Mesophyll conductance (g m ) describes the ability of CO 2 to diffuse across the interior of the leaf. In plants with C 3 photosynthesis, g m is roughly similar in magnitude to stomatal conductance (g s ), frequently accounting for about 40% of the decline in CO 2 concentration from the ambient atmosphere to the chloroplasts (C c ) (Flexas et al. 2008;Warren 2008a). As a consequence, it has an important place in leaf-level photosynthesis models (von Caemmerer 2000;Dewar et al. 2017), but has been so infrequently quantified that it is seldom included in earth-system models (Rogers et al. 2017). It also has a critical role in the inference of water-use efficiency (WUE) from stable carbon isotope composition (δ 13 C) of plant tissues or, conversely, in the inference of δ 13 C from gas exchange (Rogers et al. 2017). This role is caused by the decrease in CO 2 concentration at the enzyme rubisco, where δ 13 C is determined, relative to the substomatal cavities, where WUE is determined. Mesophyll conductance provides a means to calculate this difference. If g m could be accounted for, then δ 13 C could provide independent tests of the WUE predictions of leaf (von Caemmerer 2000;Wei et al. 2014), canopy (Keenan et al. 2013), and earth-system models (Rogers et al. 2017). One reason for the relative paucity of g m data is that it is more difficult to estimate than g s . Stomatal conductance to CO 2 is easily estimated from humidity, temperature and transpiration measurements, which might come from leaflevel gas exchange or sap-flux data. Given the relative ease of making such measurements, high temporal resolution g s data are available for many species and sites, and models of g s based on theory and empirical data have converged (Medlyn et al. 2011) and been incorporated into global models (Prentice et al. 2014;Rogers et al. 2017). In contrast, measuring g m requires simultaneous measurements of gas exchange and either chlorophyll fluorescence or photosynthetic discrimination against 13 C (∆ 13 C). Discrimination can be inferred from the δ 13 C signature of photosynthesis products, e.g. leaf soluble sugars, phloem contents, plant tissues (e.g.: Hu et al. 2010;Ubierna and Marshall 2011), or directly from leaf CO 2 flux (e.g.: Evans et al. 1986;Warren et al. 2003;Bickford et al. 2009;Wingate et al. 2007Wingate et al. , 2010Maseyk et al. 2011;Campany et al. 2016). These methods are technically challenging, especially under field conditions, so that measurements are often made with low temporal resolution.
It has been difficult to model g m , because previous studies have found that g m and g s respond differently to changes in environmental conditions, suggesting that the two are not tightly coupled. Rapid responses of g m have been described to several environmental variables (for a review see Flexas et al. 2008;Warren 2008a;Flexas et al. 2012). These variables include light intensity or quality (Flexas et al. 2007;Tholen et al. 2008;Hassiotou et al. 2009;Loreto et al. 2009;Campany et al. 2016), intercellular CO 2 concentration (C i ) (Flexas et al. 2007;Hassiotou et al. 2009;Vrábl et al. 2009;Bunce 2010;Douthe et al. 2011;Tazoe et al. 2011), and leaf temperature (Bernacchi et al. 2002;Yamori et al. 2006;Warren 2008b;Evans and von Caemmerer 2013). If g s responded to other variables, or at different rates, then the ratio g m /g s would change. For example, it has been shown that g m responds similarly, but more quickly, to variable C i than g s (Flexas et al. 2007). In addition, the g m /g s ratio was found to be temperature dependent in a study exploring the thermal acclimation of g m in spinach (Yamori et al. 2006).
Vapour pressure deficit (VPD) is particularly interesting in this context, because g s responds so strongly to it (Marshall and Waring 1984;Oren et al. 1999;Medlyn et al. 2011). In contrast, the response of g m to VPD has not been extensively studied and the results so far are contradictory (Bongi and Loreto 1989;Warren 2008c, Loucos et al. 2017. Both temperature and VPD change dynamically under natural conditions, diurnally and seasonally, potentially influencing the g s to g m relationship. However, the magnitude and importance of this variability has yet to be explored. Given constant g s , an increase in g m would increase wateruse efficiency (WUE) (Flexas et al. 2010;Galmés et al. 2011), which is defined as the ratio of net carbon assimilation (A net ) to water loss through transpiration (E). This would happen because an increase in g m has no direct effect on transpiration, but it increases photosynthesis, resulting in an increase of the A net /E ratio. Accounting for g m is especially important when estimating WUE from δ 13 C. For example, WUE is often inferred from historic tree-ring isotope data (Marshall and Monserud 1996;Seibt et al. 2008;Voelker et al. 2016). Such inferences require that some value for g m be assumed. This assumption is often embedded as a constant, empirical adjustment in the relationship between 1 3 C i /C a and isotopic discrimination (Farquhar et al. 1982), or extrapolated based on its correlation with g s in models of WUE (Klein et al. 2015), although as noted above, the correlation with g s is not always strong.
In this manuscript, we present continuous, simultaneous measurements of shoot-scale gas exchange and 13 C discrimination in a 100-year-old Pinus sylvestris stand in northern Sweden. We use these simultaneous data streams to obtain hourly g m estimates parallel to g s , A net and E. We begin with a brief description of how the data were treated and evaluate the accuracy of our measurement system. We next explore the diurnal dynamics of g s and g m and their relationship to A net . Finally, we compare estimates of WUE derived from gas exchange (WUE G ) with estimates derived from photosynthetic discrimination (WUE ∆ ). Three photosynthetic discrimination (∆ 13 C) models were used to calculate WUE ∆ : a comprehensive model, a partial model and a simple model. Additionally, the comprehensive model was applied using three different assumptions for g m values. We compare the different models and calculations and discuss their impact on WUE ∆ estimates.

Description of the experimental site
The study was conducted in a ~ 100-year-old, naturally regenerated, even-aged stand of Pinus sylvestris (Scots pine) at the Rosinedalsheden experimental forest in northern Sweden (64°10′N, 19°45′E, 153 m above see level), during the growing season of 2017. The Rosinedalsheden experiment includes an intensive fertilisation treatment (Lim et al. 2015), but the current study was conducted entirely on the unfertilised area. The photosynthetic season typically extends from mid-April to mid-November, buds burst at the end of May, and stem diameter-growth ceases in late August (Tarvainen et al. 2018). The June to August mean temperature was 12.4 ± 0.8 °C (mean ± SD) and the mean monthly precipitation was 67.9 ± 8.6 mm (mean ± SD), based on the 15-year (2003-2017) data measured at the Vindeln-Sunnansjönäs meteorological station (Swedish Meteorological and Hydrological Institute, www.smhi.se) approximately 5 km from the experimental site. The site has weakly podzolised fine sandy soil with a thin (2-5 cm) organic layer (Hasselquist et al. 2012). The leaf area index was 2.7 and the average tree height was 18.6 ± 2.3 m (mean ± SD) in 2013 (Lim et al. 2015).

Experimental setup for continuous measurements of gas exchange
Shoot gas exchange (CO 2 and H 2 O) was measured continuously on one 1-year-old upper canopy shoot on four trees.
A 16-m tall scaffolding tower was used to reach the shoots and secure the equipment. The shoot-scale gas exchange was measured using a custom-built multichannel gas exchange system (GUS) (Wallin et al. 2001;Tarvainen et al. 2016), equipped with infrared gas analysers (IRGA, CIRAS-1, PP systems Hitchin Herts, U.K.) to measure CO 2 and H 2 O partial pressure in the air from shoot cuvettes and reference channels. The 330 ml shoot cuvettes had a transparent acrylic plastic (Plexiglas) top for natural illumination. The cuvettes were temperature (T) controlled to track the ambient T and were equipped with a light sensor (PAR-1 M, PP systems, Hitchin, Herts, UK). The polyethylene tubing that connected the cuvettes to the IRGAs were insulated and heated with cables to avoid condensation. Nonetheless, morning condensation could occur in the cuvettes in connection with heavy rain events; we filtered those days out in the current analysis. The GUS cycled through the four shoot cuvettes and two non-cuvette lines once per hour, spending 7 min at each position, which were divided into 2 min of waiting time to allow instrument readings to stabilise and 5 min of measurement. We used the means from the 5-min measurement periods in the subsequent analyses, which yielded approximately one value/cuvette/hour throughout the 9 days. The non-cuvette lines were used for data quality assurance and for measurement of δ 13 C of ambient air (see details in next chapter). The IRGAs were calibrated with 400 µmol mol −1 CO 2 gas at the beginning and at the end of the growing season. Additionally, every hour the IRGAs were zero calibrated and the system ran a cross-calibration protocol to match values in the sample and reference channels.

Continuous measurement of δ 13 C
The isotopic composition of the CO 2 in the air entering and leaving the cuvettes was analysed with a cavity ring-down spectrophotometer (CRDS; G2131-i, Picarro Inc., California, USA). The CRDS was connected to the same central line as the GUS, in parallel to the sample IRGA. We tested the instrument at varying CO 2 and H 2 O vapour concentrations and found that the δ 13 C values were dependent on both, with an asymptotic relationship of δ 13 C to CO 2 concentration (Fig. S1) and a linear dependency to H 2 O vapour concentration (Fig. S2). The continuous δ 13 C readings were corrected to account for the CO 2 and H 2 O concentration effects before the data were used in further analyses. The CRDS was factory-calibrated in 2017 and manually calibrated once per week, using two reference gases with known CO 2 concentrations (411 µmol mol −1 , SD = 5.1; 1606 µmol mol −1 , SD = 13.1) and δ 13 C values (− 32.36‰, SD = 0.09; − 4.14‰, SD = 0.06). The reference gases were analysed at the SLU Stable Isotope Laboratory (Umeå, Sweden) with GB-IRMS (Gasbench II-Isotope Ratio Mass Spectrometer, Thermo Fisher Scientific, Bremen, Germany), which was calibrated against IAEA-co-9 and NBS 19 standards. We found the weekly calibrations to be sufficient, because the reference δ 13 C values were stable over the season (Fig. S3) and were offset from the reference gases by a constant 4.17‰ (SD = 0.1), after correction for CO 2 concentration. The CRDS recorded δ 13 C values once per second during the 5-min calibration period, which were then combined into a mean for each calibration date and these means yielded standard deviations of 0.1‰ for δ 13 C.

Calculation of leaf gas exchange parameters and mesophyll conductance
In this paper, we present data collected on nine sunny days during the summer (28th of June-2nd of July and 6th of July-9th of July), with daily minimum and maximum temperatures of 6.2 ± 0.5 °C and 24.4 ± 0.6 °C, respectively, and daily maximum irradiation of 1964 ± 25 µmol m −2 s −1 . Because of the high latitude and season, sunrise was typically around 02:15 and sunset was around 23:00. These days were chosen for high photosynthetic rates and lack of condensation in the cuvettes and tubing. We optimised the system setup to yield clear and consistent δ 13 C values with the CRDS, using 5-min integrations at approximately 1-second intervals. Because each of these measurements contributed to the mean δ 13 C value, it was appropriate to calculate the standard error of the mean from them. This yielded high precision, typically SE < 0.06‰.
A net , E, g s , and C i were calculated from the gas exchange data according to the model described by Farquhar et al. (1980). Boundary layer conductance has previously been found to be high (8.1 mol H 2 O m −2 s −1 ) (Uddling and Wallin 2012) in our gas exchange cuvettes, therefore, we assumed boundary layer resistance to be insignificant. Needles from the shoots enclosed in the cuvettes were collected at the end of the study campaign to determine the projected leaf area using a flat bed scanner (Epson 1600) equipped for dual scanning, and WinSEEDLE Pro 5.1a (Regent Instruments, Canada) analysis software.
Mesophyll conductance (g m ) and C c were estimated from the carbon isotope discrimination data collected by the CRDS. The g m was calculated from the comprehensive ∆ 13 C model of Farquhar and Cernusak (2012) that includes ternary corrections. In particular, we used the formulation of Evans and von Caemmerer (2013) (see supplementary materials for details) that calculates g m as where b, a m and e are the fractionation factors during carboxylation (b = 29‰), dissolution and diffusion through water (a m = 1.8‰) and respiration (e, see Eqn. S5), respectively. R d is daytime respiration (Eqn. S1), and C out 1 is the CO 2 concentration in the cuvette; ∆ i , ∆ o , ∆ e and ∆ f are, respectively, the discrimination when C i = C c (Eqn. S2), the observed discrimination during gas exchange (Eqn. S3 and S4), the discrimination associated with respiration (Eqn. S5 and S6) and with photorespiration (Eqn. S7). The term t is the ternary correction factor (Eqn. S8, Farquhar and Cernusak 2012). Note that C out is lower than the atmospheric CO 2 concentration (C in ), due to A net within the cuvette. The CO 2 concentration at the site of carboxylation (C c ) was calculated from g m through the following relationship: We evaluated how the magnitude of the net photosynthetic CO 2 drawdown, calculated as C in −C out , affected our estimates of C c . This drawdown, together with instrument precision, determines the error associated with ∆ 13 C measurements, which ultimately determines the error in C c and g m estimates (for a discussion see Ubierna et al. 2018). The concentration drop is evaluated with the parameter ζ = C in / (C in −C out ). Pons et al. (2009) showed that the error associated with g m estimates increased when ζ was large and the instrument precision was low. We likewise found that C c became exponentially more variable as the CO 2 drawdown in the cuvette decreased below 20 μmol CO 2 mol −1 (Fig. 1a). Assuming an ambient CO 2 concentration of 400 ppm, a drawdown of 20 μmol CO 2 mol −1 corresponds to ζ = 20 (= 400/(400-380)). In this case, and with an instrument precision of 0.06‰ the error associated with ∆ 13 C measurements was 1.7‰ (= √ 2 ⋅ ⋅ Precision) . This low drawdown and large error mainly occurred during early mornings and evenings, so that it was not possible to acquire reasonable estimates before 04:00 and after 20:00 (Fig. 1b). For most of the day, the observed drawdown was substantially greater than 20 μmol CO 2 mol −1 which resulted in ζ < 10 and associated errors in ∆ o < 0.8‰ (Fig. 1b).

Comparison of models to estimate water-use efficiency from ∆ 13 C
Instantaneous WUE can be derived from ∆ 13 C (WUE ∆ ) or from gas exchange (WUE G ) measurements as (Seibt et al. 2008;Hu et al. 2010;Wang et al. 2014;Klein et al. 2015;Guerrieri et al. 2016): (2) where C i is solved from a theoretical ∆ 13 C model.
We considered three models for ∆ 13 C, which resulted in three estimations of WUE ∆ . First we estimated C i from the simple model by Farquhar et al. (1982), as where b is taken as 27‰, a standard value for C 3 plants, that was derived empirically from relationships between δ 13 C of leaf bulk material and C i /C a values (Farquhar et al. 1982;Cernusak et al.2013;Ubierna and Farquhar 2014). This model does not account specifically for the dependency of ∆ 13 C on g m , R d or photorespiration (R p ); instead it includes these effects empirically within b , which is often sufficient in practice (Cernusak et al. 2013;Bloomfield et al. 2019). Second, we estimated C i from a model proposed by Seibt et al. (2008), subsequently referred to as the partial model, as where Γ* is the CO 2 compensation point, derived from an Arrhenius function (Bernacchi et al. 2001;Medlyn et al. 2002 Eq. 12). This model accounts explicitly for the effect of g m and R p and assumes negligible effect of R d . Finally, from the comprehensive model of Farquhar and Cernusak (2012) C i can be solved as (see supplemental materials in Cernusak et al. 2018 where equations I, II and III are given in the supplementary materials (Eqn S9-S11). This model accounts explicitly for g m , R p and R d , and it includes a correction for the ternary effect.
To avoid circularity, we divided our data set into two parts. We used 4 days' data to estimate a mean value of g m (0.29 mol CO 2 m −2 s −1 bar −1 ). Subsequently, this mean g m was used on the remaining 5 days' data to estimate C i from ∆ 13 C (Eqs. 4, 5 and 6) and WUE (Eq. 3). Note that the 4-day mean g m was slightly different from the mean for all 9 days together, which was 0.31 mol CO 2 m −2 s −1 bar −1 . For the comprehensive model, besides using a constant mean g m , we also performed the calculations using either a constant g m /g s (2.9) or infinite g m and compared these estimates as well to WUE G .

Data analysis
A statistical filter was applied to the dataset to discard outliers in C i −C c and g m . Any data point outside the range of mean ± 3 SD was considered an outlier and removed. This filter removed 4.5% of the data. Despite the filtering, some few negative conductances remained. Although they are not theoretically possible, we retained them in the analysis because they represent the tails of the statistical distributions and they influenced the means. The sole exception was when we analysed the dependency of net photosynthetic rates on the conductances. In this one analysis, the negative values were deleted. The four cuvettes were treated as biological Fig. 1 a Standard deviation of the CO 2 concentration in the chloroplast (C c ) in relation to CO 2 drawdown in the cuvette, defined as the difference between the atmospheric concentration (C in ), and the concentration inside the cuvette (C out ). The SD of C c was estimated for every 2 µmol mol −1 change in the CO 2 drawdown. The figure is based on non-filtered data. b The diurnal time course of the CO 2 drawdown. The whiskers of the box-plots extend to 1.5 times the interquartile range. The grey area marks the time of day excluded from the analysis. The figure is based on non-filtered data replicates, from which the mean hourly values were used for further analysis. Regression analysis was used to evaluate diurnal patterns. This included linear, polynomial, and nonlinear regression, as deemed appropriate. Correlations were treated as significant for p ≤ 0.05. All variability is given as standard error, unless stated otherwise. All statistical analyses were performed using the base package of R (version 3.3.2).

Diurnal trends of g s and g m
We evaluated the diurnal trends in stomatal and mesophyll conductance, and in their ratio. Mean g s was 0.115 (SE = 0.002) mol CO 2 m −2 s −1 bar −1 . As expected, g s showed a significant diurnal pattern (F = 79.17, p < 0.001), with peak values between 09:00 and 10:00, and decreased thereafter (Fig. 2a). We found a mean g m value of 0.31 (SE = 0.02) mol CO 2 m −2 s −1 bar −1 . Furthermore g m also had a significant diurnal pattern (F = 13.52, p < 0.001; Fig. 2b) with relatively stable mean values between 08:00 and 16:00 and lower values in the early morning and towards the evening. The mean for the unitless ratio g m /g s was 2.67 (SE = 0.3); with a weak, but significant diurnal pattern (F = 3.9, p = 0.02).

The relationship of A net to g s and g m
A net followed a typical diurnal pattern, with highest rates between 08:00 and 12:00, with a mean of 16.2 (SE = 0.26) µmol CO 2 m −2 s −1 , and gradually declining rates in the afternoon (Fig. 2c). We found a significant asymptotic relationship between A net and g s (p < 0.001, R 2 = 0.53, Fig. 3a). Similarly there was a significant asymptotic relationship between A net and g m (p < 0.001, R 2 = 0.28, Fig. 3b).

Relationship of g s and g m to VPD
The average hourly VPD varied from 0.26 kPa to 1.82 kPa during the day, with sharp increase during the mornings until about 12:00 ( Fig S4). We found a significant linear relationship between g s and VPD (F = 37.6, p < 0.001, R 2 = 0.26) (Fig. 4a) but no relationship between g m and VPD (F = 1.12, p = 0.3, R 2 = 0.001) (Fig. 4b).

Contrasting estimates of WUE from ∆ 13 C
We compared the performance of the three models to estimate WUE from ∆ 13 C (WUE ∆ ) against direct measurements of WUE as A net /E by the gas exchange system (WUE G ). Theoretically WUE ∆ and WUE G should be identical with an ideal fit, where slope m = 1 and intercept a = 0. Using the simple model resulted in a poor fit to our data (Fig. 5a). Further analysis revealed that this model could not predict WUE G in the early hours (04:00-08:00), but fit the data well between 08:00 and 20:00 (a = − 0.4, m = 1.0, R 2 = 0.69, Fig  S5). The partial model consistently overestimated WUE G by ca. 15% with no diurnal pattern (Fig. 5b). The comprehensive model matched the data well on average (Fig. 5c), but had a slight tendency to overestimate WUE G in the low range and underestimate it in the high range. Furthermore, it introduced more variability into the estimates compared Fig. 2 Diurnal variation in a stomatal conductance (g s ), b mesophyll conductance (g m ), and c net photosynthesis (A net ). The points represent the cuvette means (n = 4) for each hour and day. The blue line is the second order polynomial fit to the data and the shaded grey area is the standard error of the fit to the partial model, with a residual standard error (SEr) of 2.7 mmol CO 2 mol H 2 O −1 (R 2 = 0.61) compared to 2.1 mmol CO 2 mol H 2 O −1 (R 2 = 0.78). In the comprehensive model, representing g m as a constant ratio to g s overestimated WUE G by ca. 9% compared to observations (a = 0.7, m = 1.05, Fig. S6a). Assuming infinite g m resulted in a poor fit to observed data (a = 0.7, m = 1.5, Fig. S6b) and an overestimation of WUE G by 49%.

Discussion
Here, we report the first g m estimates for mature Pinus sylvestris, one of the most widespread coniferous species of the northern hemisphere. Our mean value (0.31, SE = 0.02 mol m −2 s −1 bar −1 ) is somewhat higher than previously reported for other Pinus species (Flexas et al. 2008), but it is within the range of values reported for various conifers (Table 1) (De Lucia et al. 2003;Flexas et al. 2008;Bown et al. 2009;Bickford et al. 2010;Han 2011;Maseyk et al. 2011;Ubierna and Marshall 2011;Veromann-Jürgenson et al. 2017). Some of this variation may be due to differences in the methods used (Flexas et al. 2008). In particular, the "variable J method", which uses simultaneous measurements of gas exchange and chlorophyll fluorescence to infer g m , generally yields lower g m values than do isotopic techniques. If we exclude the "variable J" estimates from the list in Table 1, then our estimate of g m matches the other values for conifers quite well. Furthermore, our estimates of δ 13 C of A net were in the range reported previously (e.g. Wingate et al. 2010) (Fig. S7), and are the first based on measurements using The good agreement encourages us to suggest that this method, which is less expensive than most alternatives, produces reliable δ 13 C measurements and is suitable for field applications. The CRDS was steady under the variable conditions of field-measurements, exemplified by the fact that we did not see any drift in the δ 13 C values of the reference gases during several weeks of continuous measurements (Fig. S3). Nevertheless, it was crucial to correct the data for the CRDS' sensitivity to changing CO 2 and H 2 O vapour concentrations. The sensitivity of isotope measurements to CO 2 concentration is a known phenomenon and is commonly corrected for in other laser technologies, like in lead alloy tunable diode lasers . Furthermore, drying the gas before isotope analysis will avoid having to correct for H 2 O concentrations dependency, which is likely to improve measurement accuracy.
We observed an asynchronous reduction in g m and g s over the day (Fig. 2a, b). This may happen because g s is under strong control by ambient VPD (Fig. 4a), whereas we found no correlation between g m and VPD (Fig. 4b).
The response of g m to VPD has only been investigated in few studies, and with contrasting results. While Bongi and Loreto (1989) and Loucos et al. (2017) found a significant negative correlation between g m and VPD, a study looking at the effect of air humidity and soil moisture (Warren 2008c) on g s and g m found a strong correlation of both The points represent the cuvette means (n = 4) for each hour and day. The blue line is the linear fit to the data, the shaded grey area is the standard error of the fit, and m is the slope of the fit. The red line represents the theoretical 1:1 fit for comparison  Flexas et al. (2008) conductances to soil moisture, while VPD only affected g s and not g m . All studies involved different species, and higher VPD ranges (1-3 kPa and 1-2 kPa, respectively) compared to our study (0.23-1.82 kPa). These discrepancies highlight the need for further investigation including a wider range of VPD conditions for Pinus sylvestris.
We fitted an asymptotic relationship of A net to g s and g m . The asymptotic response agrees with theoretical expectations of CO 2 saturation at high conductances. In a diurnal context, A net was maintained at high rates until midday, despite declining g s from mid-morning (Fig. 2). We suggest that high g m helped to maintain A net during the late morning, enabling high C c and compensating for the decline of g s . This diurnal asynchrony between g s and g m is qualitatively similar to the observations by Theroux-Rancourt et al. (2014) on hybrid poplar cuttings exposed to soil drying over 12 days. They suggested based on daily measurements of g s and g m that a delayed g m response reduced the decline in photosynthesis and enhanced WUE during the beginning of the drought treatment. Our finding suggests, that even within a diurnal context, the asynchronous response of g m and g s to environmental conditions has significant influence on A net and presumably WUE.
We compared three models to estimate WUE from δ 13 C. We found that the simple model can estimate WUE well for most of the day. This model uses b , an empirical value that accounts for the drop of concentration between C i and C c , the different fractionations occurring during photosynthetic discrimination, as well as possible postphotosynthetic discrimination. Many studies have shown that b works well as an approximation (e.g. Farquhar et al. 1982;Seibt et al. 2008;Bloomfield et al. 2019). However, it performed poorly during the early morning, when WUE (Fig. S8), and especially δ 13 C of photosynthesis (Fig. S7) were more variable. This meant that it produced unreliable WUE estimates for 25% of the photosynthetically active period of the day. Our analysis clearly shows that a more complete model that accounts explicitly for the effects of photorespiration, or both photorespiration and daytime respiration, performs better under such variable conditions and provides more accurate estimates of WUE. The relatively high variability in the estimates highlight the need to further refine some of the model assumptions.
We have shown that it is critical to account for g m in the estimation of WUE from ∆ 13 C. This point has been made before (Seibt et al. 2008;Klein et al. 2015), but is still often neglected. Our data is yet an other example of WUE being overestimated if g m is assumed to be infinite, and we show that assuming constant g m /g s or constant g m both yield better estimates than infinite g m . Estimating WUE from g m /g s had the further advantage of accounting for some of the diurnal change in g m , resulting in a slope closer to 1 than when g m was assumed constant.
Nevertheless, this approach does not take into account the diurnality of g m /g s itself, and neglects the fact that g m is much less strongly correlated with VPD than g s .
The current study presents the first estimate of g m for mature Pinus sylvestris trees, one of the most wide-ranging tree species in the world. Those estimates were derived with a CRDS/gas exchange system, which presents opportunities for simplifying the measurement of online ∆ 13 C discrimination. The measurements were made continuously and in the field over several sunny days in the summer. The high temporal resolution of our data allowed us to evaluate diurnal trends in conductance in relation to A net , and test different models to estimate WUE form ∆ 13 C. Our analysis revealed that the simple model to account for 13 C discrimination worked well, but only under stable conditions, and that the comprehensive model has the potential to account for variable conditions and provide reliable estimates of C i and WUE. We highlight the need for further work under a broader range of environmental conditions, and including seasonal phenology. Our g m estimate provides a means of improving inferences of WUE from ∆ 13 C and our continuous measurements provide a path forward to improve the modelling of g m in the future.