Explicitly accounting for needle sugar pool size crucial for predicting intra‐seasonal dynamics of needle carbohydrates δ18O and δ13C

Summary We explore needle sugar isotopic compositions (δ18O and δ13C) in boreal Scots pine (Pinus sylvestris) over two growing seasons. A leaf‐level dynamic model driven by environmental conditions and based on current understanding of isotope fractionation processes was built to predict δ18O and δ13C of two hierarchical needle carbohydrate pools, accounting for the needle sugar pool size and the presence of an invariant pinitol pool. Model results agreed well with observed needle water δ18O, δ18O and δ13C of needle water‐soluble carbohydrates (sugars + pinitol), and needle sugar δ13C (R 2 = 0.95, 0.84, 0.60, 0.73, respectively). Relative humidity (RH) and intercellular to ambient CO2 concentration ratio (C i/C a) were the dominant drivers of δ18O and δ13C variability, respectively. However, the variability of needle sugar δ18O and δ13C was reduced on diel and intra‐seasonal timescales, compared to predictions based on instantaneous RH and C i/C a, due to the large needle sugar pool, which caused the signal formation period to vary seasonally from 2 d to more than 5 d. Furthermore, accounting for a temperature‐sensitive biochemical 18O‐fractionation factor and mesophyll resistance in 13C‐discrimination were critical. Interpreting leaf‐level isotopic signals requires understanding on time integration caused by mixing in the needle sugar pool.


New Phytologist Supporting Information
The following Supporting Information is available for this article:       Tarvainen et al. (2013); c temperature response function (Bernacchi et al., 2001) fitted to night-time shoot chamber data Methods S1 Modeling shoot gas exchange The exchange of water vapor (E , mol m −2 s −1 ) and CO 2 (A n , µmol m −2 s −1 ) between the shoot and air follow where g b , g s and g m (mol m −2 s −1 ) are boundary layer, stomatal, and mesophyll conductance for CO 2 , respectively; 1.6 is the ratio of molecular diffusivity of water vapor to that of CO 2 in air; w a , w s and w i (mol mol −1 ) are mole fractions of water vapor in the atmosphere, at the leaf surface and inside the leaf, respectively; C a , C s , C i and C c (µmol mol −1 ) are CO 2 mole fractions in the atmosphere, at the leaf surface, inside the leaf, and in the chloroplast, respectively. In the model, we assume vapor pressure inside the leaf is saturated and that the leaf is at air temperature.
Following the photosynthesis model of Farquhar et al. (1980), net leaf CO 2 exchange is given as where A c and A j (µmol m −2 s −1 ) are Rubisco-and RuBP regeneration-limited assimilation rates, respectively, and r d (µmol m −2 s −1 ) is mitochondrial respiration. The Rubisco-limited rate is defined as where V cmax (µmol m −2 s −1 ) is the maximum rate of Rubisco activity, Γ * (µmol mol −1 ) is the CO 2 compensation point in the absence of mitochondrial respiration, K c and K o (µmol mol −1 ) are the Michaelis-Menten constants for CO 2 and O 2 , respectively, and O is the oxygen mixing ratio (2.1 × 10 5 µmol mol −1 ). The RuBP regeneration-limited rate follows where the irradiance response of the rate of electron transport J (µmol m −2 s −1 ) is modeled by where θ (-) is the curvature of the response of electron transport to irradiance, J max (µmol m −2 s −1 ) is the potential electron transport rate, and I (µmol m −2 s −1 ) is the photosynthetically active radiation (PAR) effectively absorbed by photosystem II. In Eqs. S4-S5, the term (1 − Γ * /C c ) is used to account for CO 2 release through photorespiration, i.e.
The temperature dependency of V cmax and J max have the general form given in Medlyn et al. (2002) and r d that in Bernacchi et al. (2001). Additionally, maximum carboxylation capacity V cmax 25 , maximum electron transport rate J max 25 , and mitochondrial respiration rate r d 25 at a reference temperature of 25°C are assumed to vary with seasonal cycle of photosynthetic capacity following a delayed temperature model (Mäkelä et al., 2008) where S max and T 0 (°C) are parameters, and the delayed temperature S (°C) is solved from d S /d t = (T dai l y − S )/τ, where T dai l y (°C) is mean daily ambient temperature and τ (days) is the time constant of the delay process.
As defined by Eq. S2, A n is additionally limited by stomatal and mesophyll conductance. Stomatal conductance (g s , mol m −2 s −1 ) is defined by the unified stomatal model relying on the principal that stomata act to minimize the amount of water used per unit carbon gained (Medlyn et al., 2011) where g s,0 (mol m −2 s −1 ) and g s,1 (kPa 0.5 ) are parameters and D (kPa) is vapor pressure deficit. Eq. S8 describes stomatal behavior when photosynthesis is active, therefore an additional parameter g s,ni g ht (mol m −2 s −1 ) is defined as a lower limit for g s . g s,ni g ht has an important role in the non-steady-state solution of leaf water δ 18 O (Ogée et al., 2009).
The behavior of mesophyll conductance (g m , mol m −2 s −1 ) is less well understood, but its role in 13 C-discrimination is widely recognized (Medlyn et al., 2017). Here, we used a g m description suggested by Dewar et al. (2018) where g m,1 (-) is a fitted parameter. Again, Eq. S9 describes only conditions when photosynthesis is active, thus g m,ni g ht (mol m −2 s −1 ) is defined as a lower limit for g m .
To account for water stress (Zhou et al., 2013;Kellomaki and Wang, 1996), V cmax 25 and g s,1 (Eq. S8) were adjusted as non-linear functions of relative plant extractable water (Launiainen et al., 2022) where R ew = (θ − θ r )/(θ s − θ r ) and b 0 and b 1 are fitting parameters. The soil water content θ (m 3 m −3 ) was measured at ca. 5cm depth in the mineral soil, where field capacity and residual water content were θ s = 0.30 m 3 m −3 and θ r = 0.03 m 3 m −3 , respectively. b 0 and b 1 were adopted from Launiainen et al. (2022), who fitted the parameters to shoot chamber data from the same site during drought year 2006 .
All parameters values applied in the modeling of shoot gas exchange at the study site are listed in Table S1.
Methods S2 Derivation of model for 13 C-discrimination of net CO 2 exchange (Eq. 8) The starting point is Eq. A2.6 in Appendix II of Wingate et al. (2007): where R subst r at e of Wingate et al. (2007) is replaced by R sug as that is our substrate for mitochondrial respiration.
Solving Eq. S11 for 13 ∆, which now appears on both sides of equation, results in: Here, the first term accounts for diffusion through stomata, carboxylation and photorespiration. However, as in Wingate et al. (2007) this part can be easily extended to cover also diffusion through the leaf boundary layer and 8 mesophyll: The derivation in Wingate et al. (2007) was based on the definition A n ′ /A n = R a (1 − 13 ∆) and r d ′ /r d = R sug (1 − e) for discrimination (where A n ′ /A n and r d ′ /r d are the isotopic ratios of net CO 2 exchange and dark respiration, respectively). Because of this, Eq. S13 reduces to R a (1 − 13 ∆) = R sug (1 − e) in dark, when k = 0, representing discrimination by dark respiration (r d ′ /r d ). However, discrimination is more commonly defined as A n ′ /A n = R a /(1 + 13 ∆) and r d ′ /r d = R sug /(1 + e) (Farquhar et al., 1989), and this is the definition that is used for 18 O-discrimination.
Deriving the classical discrimination equation (Farquhar et al., 1982) based on this formulation is less complex and requires fewer second-order approximations (Farquhar et al., 1989). To be in line with the more common formulation for discrimination, and use consistent definitions of discrimination for both 13 C and 18 O, the r d -term (last term in Eq. S13) needs to be modified so that in dark Eq. S13 reduces to R a /(1 + 13 ∆) = R sug /(1 + e). As a function of 13 ∆, this is expressed as: where the right-hand side corresponds to the modified r d -term of Eq. 8: Although inserting Eq. S14 into Eq. S13 to obtain Eq. 8 can be considered as a shortcut in the derivation, it is the simplest way to ensure that Eq. 8 converges to Eq. S14 when k tends to zero, given the definition we used for discrimination ( 13 ∆ and e). In practice, using our Eq. 8 or Eq. S13 adopted from Wingate et al. (2007) with the corresponding definitions for discrimination, has little impact on the modeling results (less than 0.5‰) and e values should be very comparable between the two studies.
For definition of symbols see main manuscript.

Methods S3 Modeling source water δ 18 O
The oxygen isotope ratio of source water (R s ) was modeled based on a mass balance approach for the soil rooting zone (Ogée et al., 2009). The rooting zone water budget is expressed as: where W soi l (kg m −2 ) is rooting zone water storage, and P , E t ot and D (kg m −2 s −1 ) are precipitation, total evapotranspiration and drainage. We applied Eq. (S16) at a daily timescale to solve D , which was the only unknown as dW soi l /d t was derived from soil moisture measurements assuming a root zone depth of 0.2 m, E t ot was available from eddy covariance, and P was measured. R s can then be solved from the budget of the rooting zone water 18 O: where R r ai n is the oxygen isotopic ratio of rainfall (measured on a monthly basis). Eq. (S17) assumes that all E t ot occurs without fractionation (cf. Ogée et al., 2009).
The resulting source water δ 18 O composition was compared against the values observed for twig water suggesting 73% of the variation of twig water δ 18 O was captured with the approach (Fig. S4). Generally measured twig water δ 18 O lie within the range measured for soil water at depths 0.02 m and 0.1 m. During times when this was not true (e.g., late September 2019), modeled values typically also deviated from the measured twig water values. Plausible reasons for this are that root uptake is from deeper layers or that twig water is not in equilibrium with soil water due to low transpiration rates.
Methods S4 Derivation of Eqs. 10-12 When the sugar pool size is taken as a constant over time and q = A n (see section 3.2), the implicit solution of Eq. 6 (or Eq. 9 when neglecting e) is: S sug (R t sug − R t −1 sug ) ∆t = (A n + r d ) t R t assi mi l at es − (A n + r d ) t R t sug (S18) where ∆t (s) is the time interval between t − 1 and t . Solving for the isotopic ratio of sugars at time t yields: R t sug = (A n + r d ) t R t assi mi l at es + (S sug /∆t )R t −1 sug S sug /∆t + (A n + r d ) t (S19) Defining α = (A n + r d )/(S sug /∆t + A n + r d ) further simplifies the formulation to that presented in Eq. 10: R t sug = α t R t assi mi l at es + (1 − α t )R t −1 sug (S20) Inserting the same formulation for the isotopic ratio of sugars at time t − 1, t − 2, ... into Eq. S20 yields: R t sug = α t R t assi mi l at es + (1 − α t ) (α t −1 R t −1 assi mi l at es + (1 − α t −1 ) (α t −2 R t −2 assi mi l at es + (1 − α t −2 ) (...))) (S21) which can be written as a weighed mean of past time instances R assi mi l at es R t sug = ∞ n=0 (w n R t −n assi mi l at es ) where w n is the weight of the signal at time t − n: To enable the calculation of weighted signals the sum in Eq. S22 was cut off at τ so that τ n=0 w n ≈ 0.95. With this cut-off, the sum of the weights is less than unity unlike in Eq. S22 and therefore we need to add the sum to the denominator resulting in the formulation of Eq. 12: (w n R t −n assi mi l at es ) τ n=0 w n (S24)