Linking canopy‐scale mesophyll conductance and phloem sugar δ13C using empirical and modelling approaches

Summary Interpreting phloem carbohydrate or xylem tissue carbon isotopic composition as measures of water‐use efficiency or past tree productivity requires in‐depth knowledge of the factors altering the isotopic composition within the pathway from ambient air to phloem contents and tree ring. One of least understood of these factors is mesophyll conductance (g m). We formulated a dynamic model describing the leaf photosynthetic pathway including seven alternative g m descriptions and a simple transport of sugars from foliage down the trunk. We parameterised the model for a boreal Scots pine stand and compared simulated g m responses with weather variations. We further compared the simulated δ13C of new photosynthates among the different g m descriptions and against measured phloem sugar δ13C. Simulated g m estimates of the seven descriptions varied according to weather conditions, resulting in varying estimates of phloem δ13C during cold/moist and warm/dry periods. The model succeeded in predicting a drought response and a postdrought release in phloem sugar δ13C indicating suitability of the model for inverse prediction of leaf processes from phloem isotopic composition. We suggest short‐interval phloem sampling during and after extreme weather conditions to distinguish between mesophyll conductance drivers for future model development.

Mitochondrial respiration rate is calculated following Launiainen et al. (2015) as where Rd,25 is mitochondrial respiration rate in 25 °C temperature, T(t) is air temperature (K), TN25 is 298.15 K, R is the molar gas constant and le represents the reduction of mitochondrial respiration in light, r1 and r2 are parameters and where Rs is the isotopic ratio of carbon in needle sugar pool ( ) and e is a 13 C discrimination parameter related to photorespiration (Ghashghaie et al. 2003).
where I is PAR (mol m -2 s -1 ) and IRT threshold PAR for respiration restriction.
The direct effect of temperature of photosynthetic rate is calculated as where Tc(t) is temperature and d1 and d2 are coefficients. Following Mäkelä et al. (2008) the lagged effect of temperature describing seasonality (S(t)) is calculated as where Smax (°C) is the threshold where temperature acclimation reaches its maximum and where Tc(t) is temperature (°C) and τs a time delay parameter.
The reduction of mesophyll conductance in descriptions 1 and 4 caused by water stress is calculated as where reduction caused by VPD (rD) is determined as where pD is a parameter. Reduction caused by soil moisture (rS) is derived following Peltoniemi where W(t) is relative extractable water and pS is a parameter.
The reduction of mesophyll conductance in descriptions 4 and 5 caused by light environment in different parts of the canopy is expressed as: (S1.14) where , and are parameters visually estimated from Sun et al. (2014).

Methods S2 Parameter sensitivity
To test the effect of parameters e and f, i.e. discrimination of mitochondrial respiration and photorespiration (eqs S1.3 and 12) we used parameter combinations "low": e = -11, f = 6, "middle": e = -6, f = 11 and "high": e = -1, f = 16, to see how the phloem sugar δ 13 C results respond to low or high respiration discrimination. The values were chosen to cover the upper and lower limits of the suggested values of e and f for several species (Ghashghaie et al. 2003, Cernusak et al. 2013, Ubierna et al. 2019. Pool ζs (Fig. 2) is the source pool of carbon for mitochondrial respiration. We set the time constant of the carbon residence time in ζs (parameter τR, eq. 14) to 24 hours which means that the carbon used for respiration is a mixture of carbon that was photosynthesized during ca. the previous day. To test the effect of this value on the δ 13 C of respired carbon we changed the value to 5 hours.
In the photosynthesis model, low temperature directly decreases the photosynthetic rate (eq. 9).
We varied the parameters d1 and d2 of eq. S1.6 to test how steeper or flatter temperature responses affect the within day or among days δ 13 C results. For this, we used combinations of parameters d1 and d2 of 0.11 and 5 vs. 0.06 and -17 for steeper and flatter response curve, respectively. For reference values of d1 and d2 (0.08 and -5), photosynthetic rate at 10 °C is decreased by 24 % compared with maximum reached at 35 °C. Using the steeper and flatter curves resulted in reductions by 37 % and 17 %, respectively.
Furthermore, we tested the sensitivity of the simulated photosynthesis rate, mesophyll conductance and daily average δ 13 C of new photosynthates on varying parameter α while keeping other parameters as estimated. We ran the model with each gm description with α increased or decreased by 5 % or 10 % of the original, gm description specific α, estimated as explained in section 2.5.7. We calculated mean and maximum differences between the model results with changed and original α over a 22 day period. For photosynthesis rate and mesophyll conductance, we calculated a relative difference, e.g. gm,test / gm,original whereas for δ 13 C of new photosynthates, we calculated the absolute difference, δ 13 Ctestδ 13 Coriginal.    respectively) and 5 % (blue and green filled circles, respectively) and model results were compared to those with α value estimated as explained in section 2.5.7. Panels a-d show the relative difference, e.g. gm,test / gm,original whereas panels e-f show the absolute difference, δ 13 Ctest -δ 13 Coriginal. Panels a, c, and e show the mean differences and panels b, d and f the maximum differences over a 22 day period.