# Temperature-sensitive biochemical 18O-fractionation and humidity-dependent attenuation factor are needed to predict δ18O of cellulose from leaf water in a grassland ecosystem

Regina T. Hirl, Jérôme Ogée, Ulrike Ostler, Rudi Schäufele, Juan C Baca

Cabrera, Jianjun Zhu, Inga Schleip, Lisa Wingate, Hans Schnyder

► To cite this version:

Regina T. Hirl, Jérôme Ogée, Ulrike Ostler, Rudi Schäufele, Juan C Baca Cabrera, et al.. Temperature-sensitive biochemical 18O-fractionation and humidity-dependent attenuation factor are needed to predict δ18O of cellulose from leaf water in a grassland ecosystem. New Phytologist, 2021, pp.1-16. 10.1111/nph.17111. hal-03114884

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# Temperature-sensitive biochemical ¹⁸O-fractionation and humidity-dependent attenuation factor are needed to predict δ¹⁸O of cellulose from leaf water in a grassland ecosystem

Regina T. Hirl<fnref n="1" />,², Jérôme Ogée² ID, Ulrike Ostler<fnref n="1" />,<fnref n="3" /> ID, Rudi Schäufele<fnref n="1" />, Juan C. Baca Cabrera<fnref n="1" /> ID, Jianjun Zhu<fnref n="1" />, Inga Schleip⁴, Lisa Wingate² ID and Hans Schnyder<fnref n="1" /> ID

Authors for correspondence:

Regina T. Hirl

Email: regina.hirl@tum.de

Jérôme Ogée

Email: jerome.ogee@inrae.fr

Hans Schnyder

Email: schnyder@wzw.tum.de

Received: 27 June 2020

Accepted: 18 November 2020

New Phytologist (2020)

doi: 10.1111/nph.17111

**Key words:** canopy conductance, grassland, isotope-enabled soil-vegetation-atmosphere transfer model (MuSICA), ¹⁸O-enrichment of cellulose oxygen isotope composition of cellulose, perennial ryegrass (Lolium perenne), relative humidity, temperature.

## Summary

* We explore here our mechanistic understanding of the environmental and physiological processes that determine the oxygen isotope composition of leaf cellulose (δ¹⁸Ocellulose) in a drought-prone, temperate grassland ecosystem.

* A new allocation-and-growth model was designed and added to an ¹⁸O-enabled soil-vegetation-atmosphere transfer model (MuSICA) to predict seasonal (April–October) and multi-annual (2007–2012) variation of δ¹⁸Ocellulose and ¹⁸O-enrichment of leaf cellulose (Δ¹⁸Ocellulose) based on the Barbour–Farquhar model.

* Modelled δ¹⁸Ocellulose agreed best with observations when integrated over c. 400 growing-degree-days, similar to the average leaf lifespan observed at the site. Over the integration time, air temperature ranged from 7 to 22°C and midday relative humidity from 47 to 73%. Model agreement with observations of δ¹⁸Ocellulose (R² = 0.57) and Δ¹⁸Ocellulose (R² = 0.74), and their negative relationship with canopy conductance, was improved significantly when both the biochemical ¹⁸O-fractionation between water and substrate for cellulose synthesis (εbio, range 26–30‰) was temperature-sensitive, as previously reported for aquatic plants and heterotrophically grown wheat seedlings, and the proportion of oxygen in cellulose reflecting leaf water ¹⁸O-enrichment (1 – pexpx, range 0.23–0.63) was dependent on air relative humidity, as observed in independent controlled experiments with grasses.

* Understanding physiological information in δ¹⁸Ocellulose requires quantitative knowledge of climatic effects on pexpx and εbio.

## Introduction

The oxygen isotope composition of plant cellulose (δ¹⁸Ocellulose) and its enrichment above source water (Δ¹⁸Ocellulose) are thought to record environmental and physiological information of great interest to a range of scientific disciplines, including functional plant ecology and climate change biology (e.g. Barbour, 2007; Battipaglia et al., 2013; Gessler et al., 2014). In particular, δ¹⁸Ocellulose or even more so Δ¹⁸Ocellulose has been discussed as an integrated proxy of past stomatal conductance (e.g. Farquhar et al., 1998; Scheidegger et al., 2000; Barbour et al., 2000b) that can provide information about environmental or climate change effects on the processes regulating the water-use efficiency of C₃ plants. However, empirical evidence for a direct link between Δ¹⁸Ocellulose and stomatal conductance is currently incomplete, which prevents the use of δ¹⁸Ocellulose time series to interpret changes in plant water use efficiency. Fundamentally, all of the

oxygen in cellulose is derived from water (DeNiro & Epstein, 1979; Liu et al., 2016). Oxygen exchange with water can occur in multiple steps in the photosynthetic carbon cycle up to the formation of sucrose (or other transport sugars), and during metabolism of these sugars in sink tissues, when cellulose is being formed (Hill et al., 1995; Farquhar et al., 1998; Barbour et al., 2005). Therefore, δ¹⁸Ocellulose depends on the oxygen isotope composition of water in sink tissues, often approximated by the δ¹⁸O of plant source water taken up by the roots (δ¹⁸Osource), and on the δ¹⁸O of leaf lamina water (δ¹⁸Oleaf), respectively. During photosynthesis, leaf transpiration enriches isotopically leaf lamina water above source water (Δ¹⁸Oleaf ≈ δ¹⁸Oleaf – δ¹⁸Osource). δ¹⁸Osource can vary dynamically and is primarily controlled by the δ¹⁸O of meteoric inputs (δ¹⁸Orain; Dansgaard, 1964; Bowen & Wilkinson, 2002), their mixing with soil water and the intensity of soil evaporation (Barnes & Allison, 1988). In addition, δ¹⁸Osource is determined by the depth distribution of

<footnote n="1">¹Lehrstuhl für Grünlandlehre, Technische Universität München, Alte Akademie 12, Freising-Weihenstephan 85354, Germany; ²UMR ISPA, INRAE, Villenave d'Ornon 33140, France;</footnote>

<footnote n="3">³Institut für Meteorologie und Klimaforschung, Atmosphärische Umweltforschung (IMK-IFU), Karlsruher Institut für Technologie (KIT), Kreuzeckbahnstraße 19, Garmisch-Partenkirchen 82467, Germany; ⁴Nachhaltige Grünlandnutzungssysteme und Grünlandökologie, Hochschule für nachhaltige Entwicklung Eberswalde, Schicklerstraße 5, Eberswalde 16225, Germany</footnote>
roots and their specific uptake intensities as well as by the effect of transpiration and root water uptake on soil water emptying and refilling dynamics (Brinkmann *et al.*, 2018; Hirl *et al.*, 2019).

Arguably, the oxygen isotope enrichment of cellulose above source water ($\Delta^{18}\text{O}_{\text{cellulose}} \approx \delta^{18}\text{O}_{\text{cellulose}} - \delta^{18}\text{O}_{\text{source}}$) has the most important physiological interest because of its link with $\Delta^{18}\text{O}_{\text{leaf}}$ and stomatal conductance. According to the Barbour-Farquhar model (Barbour & Farquhar, 2000),

$$ \Delta^{18}\text{O}_{\text{cellulose}} = \Delta^{18}\text{O}_{\text{leaf}}(1 - p_{\text{ex}}p_{\text{x}}) + \varepsilon_{\text{bio}}. \qquad \text{Eqn 1} $$

The product $p_{ex}p_{x}$ reflects the proportion of oxygen in cellulose derived from source water, where $p_{ex}$ is the proportion of exchangeable oxygen in the intermediates formed during cellulose synthesis from sucrose exported from leaves, and $p_{x}$ is the proportion of source water at the site of cellulose formation. In other words, $1 - p_{ex}p_{x}$ represents the proportional effect of leaf lamina water $^{18}$O-enrichment on the $^{18}$O-enrichment of cellulose. $\varepsilon_{bio}$ is the average biochemical fractionation between the organic substrate for cellulose synthesis and water (Sternberg *et al.*, 1986; Barbour, 2007).

Equation 1 relies on the assumption that $\Delta^{18}\text{O}_{\text{leaf}}$ represents the $^{18}$O-enrichment of water in isotopic equilibrium with leaf sucrose, as supported by two laboratory studies on castor bean (Barbour *et al.*, 2000a; Cernusak *et al.*, 2003). In those studies, conducted in climate-controlled, steady-state conditions, the $^{18}$O-enrichment of sucrose above source water ($\Delta^{18}\text{O}_{\text{sucrose}}$) was well approximated by $\Delta^{18}\text{O}_{\text{leaf}} + \varepsilon_{bio}$, with $\varepsilon_{bio}$ set to 27‰. However, a recent study by Lehmann *et al.* (2017) on two C$_{3}$ grass species indicated that newly formed sucrose might not always be in isotopic equilibrium with average leaf lamina water. Moreover, in submerged aquatic plants (where $\Delta^{18}\text{O}_{\text{leaf}}$ is c. 0) $\varepsilon_{bio}$ was found to be inversely related to growth temperature, with a particularly strong temperature dependence below about 20°C (Sternberg & Ellsworth, 2011). Virtually the same temperature-sensitivity of $\varepsilon_{bio}$ was found in wheat seedlings during heterotrophic growth (Sternberg & Ellsworth, 2011). Although there is a likelihood that this result applies to autotrophic terrestrial plants, it is difficult to prove because it cannot be verified, as $p_{ex}p_{x}$ and $\varepsilon_{bio}$ cannot be measured simultaneously.

Probably, the least contentious parameter in Eqn 1 is $p_{x}$, at least in nontranspiring tissue such as the leaf-growth-and-differentiation zones of grasses or the developing cells of tree trunks, where $p_{x}$ has been shown to stay close to 1 (Cernusak *et al.*, 2005; Liu *et al.*, 2017a). Sucrose is the most common carbohydrate transported within plants (Lalonde *et al.*, 2003) and the main substrate from which UDP-glucose, the immediate precursor of cellulose synthesis, is formed in heterotrophic tissue (Verbancic *et al.*, 2018), such as the leaf growth zone of grasses (Baca Cabrera *et al.*, 2020). Based on theoretical considerations of oxygen exchange between the metabolites of sucrose and water during cellulose formation and on observational data, the value of $p_{ex}$ is often assumed to be around 0.4 (Sternberg *et al.*, 1986; Roden & Ehleringer, 1999; Barbour & Farquhar, 2000; Cernusak *et al.*, 2005), but considerable variation in $p_{ex}$ has been suggested from

other observational studies (Gessler *et al.*, 2009; Song *et al.*, 2014; Cheesman & Cernusak, 2017). As it cannot be measured *in vivo*, estimates of $p_{ex}$ must be obtained as a fitted parameter, whilst assuming values for $p_{x}$ and $\varepsilon_{bio}$. Such estimations are sensitive to errors, including any effect of isotopic disequilibrium between $\Delta^{18}\text{O}_{\text{sucrose}}$ and $\Delta^{18}\text{O}_{\text{leaf}}$ (Lehmann *et al.*, 2017). Higher isotopic disequilibria between leaf lamina water and sucrose have also been found when air relative humidity (RH) was lower (Lehmann *et al.*, 2017). When interpreted with Eqn 1, this latter result suggests that $p_{ex}p_{x}$ may increase with increasing RH. A positive relationship between RH and $p_{ex}p_{x}$ was also suggested by the relationship between $\Delta^{18}\text{O}_{\text{cellulose}}$ and $\Delta^{18}\text{O}_{\text{leaf}}$ in the studies of Liu *et al.* (2016) and Helliker & Ehleringer (2002a) for a range of C$_{3}$ and C$_{4}$ grasses, perhaps pointing to isotopic disequilibria between $\Delta^{18}\text{O}_{\text{sucrose}}$ and $\Delta^{18}\text{O}_{\text{leaf}}$ also in these cases. Clearly, there remain important knowledge gaps on the effect of environmental conditions on $\varepsilon_{bio}$ and $p_{ex}p_{x}$ and, hence, their implication for physiological interpretation of $\delta^{18}\text{O}_{\text{cellulose}}$ or $\Delta^{18}\text{O}_{\text{cellulose}}$ from field studies.

The temporal integration of all processes involved in the making of leaf cellulose (i.e. assimilation, mobilization of stored substrate, allocation of substrate to growth, and cellulose synthesis) represents an additional challenge when interpreting $\delta^{18}\text{O}_{\text{cellulose}}$ or $\Delta^{18}\text{O}_{\text{cellulose}}$ (Hemming *et al.*, 2001; Damesin & Lelarge, 2003; Gessler *et al.*, 2009, 2014; Royles *et al.*, 2013; Liu *et al.*, 2017b). In intensively managed grassland, shoot biomass is mostly vegetative and consists of short-lived leaves (Lemaire *et al.*, 2000). Leaf production during the growing season is continuous, with new leaf production occurring simultaneously with the senescence of older leaves (Schleip *et al.*, 2013). Accordingly, the mean live leaf age (measured in growing-degree-days (GDD)) changes relatively little during the course of the vegetation period (Lemaire *et al.*, 2000; Schleip *et al.*, 2013). In a controlled environment study with *Cleistogenes squarrosa* (a perennial C$_{4}$ grass), Liu *et al.* (2017b) found a close linear relationship between the fraction of remaining leaf elongation and the fraction of oxygen in cellulose assimilated following a change of RH in the growth environment, as inferred from $^{18}$O-abundance measurements. Similar results were previously obtained by Helliker & Ehleringer (2002b), highlighting the potential of grass leaves as recorders of environmental signals in $\delta^{18}\text{O}_{\text{cellulose}}$. In light of this, allocation-and-growth models, coupled with isotope-enabled process-based models of soil-vegetation-atmosphere CO$_{2}$ and H$_{2}$O exchange, may be very useful tools for analysing the mechanisms and dynamics controlling $\Delta^{18}\text{O}_{\text{cellulose}}$ and $\delta^{18}\text{O}_{\text{cellulose}}$ in natural environments. Such models have already been applied to trees rings (Roden *et al.*, 2000; Barbour *et al.*, 2002; Ogée *et al.*, 2009; Keel *et al.*, 2016; Lavergne *et al.*, 2017), but are presently unavailable for grassland.

The present study explores the effects of environmental drivers on the parameters of the Barbour & Farquhar (2000) model (Eqn 1), used to predict $\Delta^{18}\text{O}_{\text{cellulose}}$ and $\delta^{18}\text{O}_{\text{cellulose}}$ of leaves produced during the growing seasons of multiple years (2007-2012) in a drought-prone pasture ecosystem. Specifically, we asked the following questions: What are the effects of environmental parameters (mainly RH, temperature and soil moisture
availability) on Δ¹⁸Ocellulose and δ¹⁸Ocellulose? Do environmen-
tally driven adjustments of pexpx (RH) or εbio (temperature)
improve predictions of observed Δ¹⁸Ocellulose and δ¹⁸Ocellulose? Is
canopy conductance reflected in Δ¹⁸Ocellulose or δ¹⁸Ocellulose? To
that end, we developed a new allocation-and-growth model suit-
able for grassland ecosystems (Fig. 1) that we incorporated into
the ¹⁸O-enabled soil-vegetation-atmosphere transfer model
MuSICA. Recently, we have parameterized MuSICA for the
studied pasture ecosystem and used that model to explore and
predict δ¹⁸Osource and δ¹⁸Oleaf in that system (Hirl et al., 2019).
Here, we first validated the combined MuSICA and allocation-
and-growth model by testing its ability to predict the labelling
kinetics of autotrophic respiration observed by Gamnitzer et al.
(2009), observed root : shoot C allocation (Schleip, 2013), and
the observed δ¹⁸Ocellulose of leaves at the study site, using integra-
tion times consistent with leaf growth dynamics observations.
We then applied the model to explore the three questions devel-
oped above.

Materials and Methods

Experimental site and sampling

The study was conducted inside pasture paddock no. 8 of
Grünschwaiige Grassland Research Station near Freising, Ger-
many (for details on site, vegetation and grazing management see
Schnyder *et al.*, 2006). Average air temperature in the study years

2007–2012 was 9.3°C, and mean annual precipitation was 753 mm (recorded at the Munich airport meteorological station). The mineral topsoil has a low water-holding capacity (66 mm plant-available field capacity) causing frequent and prolonged drought periods (Hirl *et al.*, 2019). The pasture was continuously grazed by Limousin suckler cows during the growing seasons (from mid-April to beginning of November). Animal stocking density was adjusted periodically to balance grass production and consumption by the cattle (Lemaire *et al.*, 2009), so that mean sward height was maintained at about 7 cm.

Two replicate leaf samples were collected at around midday (between 11:00 and 16:00 h Central European Summer Time) at approximately fortnightly intervals during the vegetation periods 2007–2012 (Hirl *et al.*, 2019). Each sample consisted of a mixed-species collection of the codominant species: four C3 grasses (Lolium perenne L., Poa pratensis L., Phleum pratense L., Dactylis glomerata L.), one rosette dicot (Taraxacum officinale F.H. Wigg.) and one legume (Trifolium repens L.). The sample included only the green, nonsenescing, fully expanded leaf blades, as well as the exposed part of the growing leaf (cf. Fig. 1 of Liu *et al.*, 2017a) from 16 vegetative tillers of L. perenne, P. pratensis and P. pratense and two vegetative tillers of D. glomerata, as well as one half of a leaf blade of T. officinale (with the midvein removed) and two trifoliate leaves of T. repens. Water in these leaf samples, along with source, soil, atmospheric humidity and rainfall samples had previously been analysed for δ¹⁸O, and presented and discussed in Hirl *et al.* (2019).

<figure><img src="image_4.png" /></figure>

**Fig. 1** Scheme of the allocation-and-growth model for predicting carbon fluxes and cellulose isotope compositions in grassland. Photosynthetic assimilation (F<sub>assim</sub>) supplies substrate with specific isotopic composition (R<sub>assim</sub>) to a well-mixed metabolic pool (W<sub>pool</sub>, with isotope ratio R<sub>pool</sub>). Maintenance respiration (F<sub>maint,resp</sub>) and allocation of substrate to growth (F<sub>growth</sub>) are both effected from the metabolic pool and thus carry the isotope signal of the pool (R<sub>pool</sub>). Partitioning between shoot and root growth (F<sub>shoot,growth</sub> and F<sub>root,growth</sub>, which involve growth respiration F<sub>growth,resp</sub> = F<sub>shoot,growth,resp</sub> + F<sub>root,growth,resp</sub>) is governed by xylem water potential (Ψ<sub>xylem</sub>). The shoot and root structural biomass pools are represented as layered (or stacked, nonmixing) pools. The integration time (d) represents the maximum age of structural leaf biomass in a sample. The size (or ‘thickness’) and isotopic composition of a given daily layer (or stack) in the shoot or root is determined by shoot and root growth rates and by the isotope ratio of the pool on that day (for details see Materials and Methods section and Supporting Information Methods S2).
Cellulose extraction and isotopic analysis

Following the procedure of Brendel *et al.* (2000) as modified by Gaudinski *et al.* (2005), α-cellulose was extracted from a subsample (50 or 25 mg) of ground plant material (for details see Liu *et al.*, 2017b). After redrying of the cellulose at 80°C for 24 h, 0.7 mg aliquots were weighed into silver cups (size: 3.3 × 5 mm, IVA Analysentechnik e.K., Meerbusch, Germany) and stored above Silica Gel orange (2–5 mm, ThoMar OHG, Liütau, Germany) in exsiccator vessels. Samples were pyrolysed at 1400°C in a pyrolysis oven (HTO, HEKAtech, Wegberg, Germany), equipped with a helium-flushed zero blank autosampler (Costech Analytical technologies, Valencia, CA, USA), interfaced (ConFlo III, Finnigan MAT, Bremen, Germany) to a continuous-flow isotope ratio mass spectrometer (Delta Plus, Finnigan MAT). A solid internal laboratory standard (cotton powder) was included after every third or fourth sample and used for V-SMOW scaling and instrument drift correction. Every sample was analysed in duplicate. All samples and the laboratory standard were measured against a laboratory working reference carbon monoxide gas, which had previously been calibrated against a secondary isotope standard (IAEA-601; accuracy of calibration ± 0.25‰ SD). The precision for the laboratory standard was < 0.3‰ (SD for repeated measurements). Oxygen isotope composition is expressed in per mil (‰) as $\delta^{18}\text{O} = (R_{\text{sample}}/R_{\text{standard}} - 1)$, with $R_{\text{sample}}$ the $^{18}\text{O}$ : $^{16}\text{O}$ ratio of the sample and $R_{\text{standard}}$ that in the V-SMOW standard.

Model

The integral model was composed of the ¹⁸O-enabled soil–vegetation–atmosphere transfer model MuSICA (Ogée *et al.*, 2003, 2009; Wingate *et al.*, 2010; Gangi *et al.*, 2015), parameterized as in Hirl *et al.* (2019), and a new allocation-and-growth model (Fig. 1). MuSICA is a multilayer multileaf model that simulates CO₂, water and energy redistribution and isotopic exchange processes in an ecosystem based on current mechanistic understanding (see Supporting Information Methods S1). MuSICA requires half-hourly climate data at a reference level above the vegetation (0.5 m here) as well as the isotopic composition of rainfall, CO₂ and water vapour at the same reference level. Meteorological variables were obtained from the meteorological station at Munich airport at about 3 km from the study site (wind speed, precipitation, air temperature, RH, air pressure), from two other meteorological stations at 10 and 12 km distance (radiation), and from an eddy flux station installed at the experimental site (CO₂ concentration) (Hirl *et al.*, 2019). For the precipitation and water vapour isotopic input data ($\delta^{18}\text{O}_{\text{rain}}$ and $\delta^{18}\text{O}_{\text{vapour}}$), we used data collected at the site whenever available, and gap-filled the data with offset-corrected IsoGSM data (Yoshimura *et al.*, 2011) as detailed in Hirl *et al.* (2019). $\delta^{18}\text{O}$ and $\delta^{13}\text{C}$ data of atmospheric CO₂ ($\delta^{18}\text{O}_{\text{CO2}}$ and $\delta^{13}\text{C}_{\text{CO2}}$) were obtained from NOAA/CMDL latitudinal products (J. Miller, pers. comm.). MuSICA parameterization included soil and vegetation properties that described the pasture system in terms of structural and hydrological characteristics, leaf gas exchange, and root

distribution and hydraulics. MuSICA, in its ‘standard parameterization’ (Hirl *et al.*, 2019), performed well in predicting $\delta^{18}\text{O}_{\text{leaf}}$, $\delta^{18}\text{O}_{\text{source}}$ (termed $\delta^{18}\text{O}_{\text{stem}}$ in Hirl *et al.*, 2019) and $\delta^{18}\text{O}_{\text{soil}}$ at different soil depths throughout seven growing seasons (2006–2012). The model also predicted the dynamics of transpiration, canopy conductance ($g_{\text{canopy}}$), root water uptake and plant-available soil water (PAW) (Hirl *et al.*, 2019). MuSICA parameters and parameters of the allocation-and-growth model were based on singular measurements (e.g. parameters of the soil water retention curve) or on measurements performed at intervals during the study period (e.g. canopy height, leaf area index). In the latter case, average observed values were used for the standard simulation, in agreement with the constant sward-state objective that ruled pasture management (see above). Missing parameters were taken from the literature (e.g. photosynthetic parameters) (see table S1 in Hirl *et al.*, 2019).

A detailed description of the new allocation-and-growth model (Fig. 1, Table 1) is provided in Methods S2. Briefly, the model includes three compartments: one well-mixed metabolic pool ($W_{\text{pool}}$) and two structural (i.e. nonmetabolic) compartments representing the aboveground shoots ($W_{\text{shoot}}$) and belowground roots ($W_{\text{root}}$), similar to Ostler *et al.* (2016). Current assimilates replenish $W_{\text{pool}}$ with rate ($F_{\text{assim}}$, gross primary production) and ¹³C and ¹⁸O signatures ($\delta^{13}\text{C}_{\text{assim}}$ and $\delta^{18}\text{O}_{\text{assim}}$, see below) predicted by MuSICA (Fig. 1). Maintenance respiration ($F_{\text{maint,resp}}$) is directly supported by $W_{\text{pool}}$, while growth respiration ($F_{\text{growth,resp}}$) is a constant fraction of growth and included in the flux of substrate allocated to the growth of shoots and roots ($F_{\text{growth}}$). $F_{\text{maint,resp}}$ is an exponential function of soil surface temperature and is assumed to be proportional to total plant carbon mass and negatively related to $W_{\text{pool}}$ when the latter decreases below a target value (Thornley & Cannell, 2000). Growth (and growth respiration) occurs only if the metabolic pool is replenished to its target value. Substrate for growth is allocated between shoot ($F_{\text{shoot,growth}}$) and root ($F_{\text{root,growth}}$) depending on root xylem water potential ($\Psi_{\text{xylem}}$), to account for the drought-sensitivity of leaf growth (e.g. Durand *et al.*, 1995), and the fractional allocation to the shoot ($f_{\text{shoot,growth}}$) is greater in spring than summer/autumn. New assimilates carry the isotopic signal of current assimilation, while the substrate supplied to growth and respiration carries the isotopic signal of the metabolic pool, assuming no isotopic fractionation during respiration or growth.

The ¹⁸O : ¹⁶O ratio of cellulose in a sample ($R_{\text{cellulose}}$) was calculated similar to Ogée *et al.* (2009), assuming that cellulose synthesis was proportional to shoot growth. The integration time in days was computed for a set thermal time by summing up daily mean soil temperature above a base temperature of 4°C (Schleip *et al.*, 2013). The biochemical fractionation ($\epsilon_{\text{bio}}$) between water and substrate used in cellulose synthesis was calculated from daily mean air temperature using the empirical function found by Sternberg & Ellsworth (2011, their fig. 2). The $p_{\text{ex}}p_x$ was calculated from midday RH of air: $p_{\text{ex}}p_x = 0.016 \text{ RH} - 0.393$ (Fig. 2), derived by regressing the differences between $\Delta^{18}\text{O}_{\text{cellulose}}$ predicted with a constant, nonbiased $p_{\text{ex}}p_x$ and observed $\Delta^{18}\text{O}_{\text{cellulose}}$ against RH (Fig. 3a) as detailed in Methods S3. The resulting function closely resembled the relationship found by Lehmann
<table><caption>**Table 1** Parameter values of the allocation-and-growth model used in Grünschwaiige pasture paddock no. 8.</caption><thead><tr><th>Parameter</th><th>Symbol</th><th>Value</th><th>Min.</th><th>Max.</th><th>Units</th><th>Comment</th></tr></thead><tbody><tr><td>Total above- and belowground dry mass</td><td>DM</td><td>270</td><td>210</td><td>350</td><td>g m<sup>-2</sup></td><td>Measured</td></tr><tr><td>Carbon content of dry mass</td><td>C</td><td>0.43</td><td>0.42</td><td>0.46</td><td>g total C g<sup>-1</sup> dry mass</td><td>Measured</td></tr><tr><td>Metabolic carbon content</td><td>w<sub>metab</sub></td><td>0.3</td><td>0.25</td><td>0.33</td><td>g metabolic C g<sup>-1</sup> total C</td><td>Ostler et al. (2016)</td></tr><tr><td>Target metabolic pool size</td><td>W<sub>pool target</sub></td><td>34.8</td><td>—</td><td>—</td><td>g metabolic C m<sup>-2</sup> soil</td><td>Calculated from DM, C and w<sub>metab</sub> (see Materials and Methods section and Supporting Information Methods S2)</td></tr><tr><td>Specific maintenance respiration</td><td>r<sub>maint,resp</sub></td><td>0.01</td><td>0.003</td><td>0.03</td><td>g respired C g<sup>-1</sup> biomass C d<sup>-1</sup></td><td>Thornley (1998)</td></tr><tr><td>Depth below or above the soil surface used for maintenance respiration scaling</td><td>d<sub>MR</sub></td><td>-5</td><td>-20</td><td>200</td><td>cm</td><td></td></tr><tr><td>Q<sub>10</sub> for maintenance respiration scaling</td><td>Q<sub>10</sub></td><td>2</td><td>1</td><td>3</td><td>—</td><td>Tjoelker et al. (2001)</td></tr><tr><td>Reference temperature for maintenance respiration scaling</td><td>T<sub>ref</sub></td><td>20</td><td>15</td><td>25</td><td>°C</td><td>Lötscher et al. (2004)</td></tr><tr><td>Ψ<sub>xylem</sub>-sensitivity of allocation</td><td>Δt</td><td>1</td><td>0</td><td>3</td><td>GDD</td><td>see Materials and Methods section, Fig. 4(c) and Methods S2</td></tr><tr><td>Integration time</td><td>Δt</td><td>400</td><td>50</td><td>600</td><td>μmol m<sup>-2</sup> s<sup>-1</sup></td><td>Rogers et al. (1998)</td></tr><tr><td>Maximum rate of carboxylation at 25°C</td><td>V<sub>cmax</sub></td><td>60</td><td>20</td><td>140</td><td>μmol m<sup>-2</sup> s<sup>-1</sup></td><td>Calculated from V<sub>cmax</sub> following Medlyn et al. (2002)</td></tr><tr><td>Potential rate of electron transport at 25°C</td><td>J<sub>max</sub></td><td>100</td><td>32</td><td>224</td><td>μmol m<sup>-2</sup> s<sup>-1</sup></td><td>Miner et al. (2017), and references therein; Wohlfahrt et al. (1998)</td></tr><tr><td>Slope of the Ball-Woodrow-Berry stomatal conductance model</td><td>m<sub>gs</sub></td><td>10</td><td>7</td><td>25</td><td>—</td><td></td></tr></tbody></table>

'Value' denotes the parameter value used in the 'standard parameterization' and 'Min.' and 'Max.' are the minimum and maximum values used in the sensitivity analyses.

et al. (2017) (Fig. 2). Alternatively, we also calculated the isotope composition of cellulose by keeping either $p_{ex}p_x$ (0.556) or $\epsilon_{bio}$ (27‰) or both $p_{ex}p_x$ and $\epsilon_{bio}$ constant.

## Statistical and sensitivity analysis

Model performance was evaluated by calculating the mean bias error (MBE = $\bar{P} - \bar{O}$, with $\bar{P}$ the mean predicted value and $\bar{O}$ the mean observed value) between observed and predicted $\delta^{18}O_{cellulose}$ (or $\Delta^{18}O_{cellulose}$), the mean absolute error ($MAE = (\sum_{j=1}^{n} |P_j - O_j|)/n$), with $P_j$ the predicted and $O_j$ the observed value of sample j, and n the number of samples (Willmott & Matsuura, 2005), and R² values. Linear regression and correlation analysis was performed to investigate the relationship between $\delta^{18}O_{cellulose}$ (or $\Delta^{18}O_{cellulose}$) and environmental parameters. All analyses were conducted in R, v.3.4.2 (R Core Team, 2017).

A sensitivity analysis was performed (1) to quantify and disentangle the effect of meteorological variables on $\Delta^{18}O_{cellulose}$ and $\delta^{18}O_{cellulose}$, and (2) to evaluate the responsiveness of $\delta^{18}O_{cellulose}$ and $\Delta^{18}O_{cellulose}$ to the parameters of the allocation-and-growth model. Two sensitivity runs were performed for each parameter or meteorological variable, using a minimum and a maximum value, based on the range of observed or expected values (see Table 1). In each sensitivity run, one parameter (or

meteorological variable) at a time was changed while all other parameters (or variables) were held the same as in the standard simulation. Regarding (1) above, the incoming short-wave radiation and wind speed, two variables that are expected to affect the leaf energy budget, were halved and doubled for each time step. Regarding (2) above, the applied parameter ranges of the allocation-and-growth model were first derived from measurements at the experimental site conducted during the study period; if no measurements were available for a parameter, relevant ranges were taken from the literature (see Table 1). Quantification of parameter effects (sensitivities) followed the procedure outlined in Hirl et al. (2019). First, systematic effects were quantified based on the 'mean sensitivity', computed as the mean difference between the sensitivity and the standard run ($\sum_{j=1}^{n} (\delta_{sens,j} - \delta_{ref,j})/n$, where $\delta_{sens,j}$ is the $\delta^{18}O_{cellulose,j}$ (or $\Delta^{18}O_{cellulose,j}$) in a sensitivity run and $\delta_{ref,j}$ is that in the standard run. Second, the variability of the parameter effect was depicted based on the standard deviation of the sensitivity, calculated from the differences between $\delta_{sens,j}$ and $\delta_{ref,j}$. To disentangle an eventual contribution of a temperature-sensitive $\epsilon_{bio}$ from the effects of other processes on the temperature sensitivity of $\Delta^{18}O_{cellulose}$, we also performed a range of sensitivity analyses in which air temperature was decreased (or increased) by 1, 3 or 5°C for all half-hourly values.
<figure><img src="image_5.png" /></figure>

**Fig. 2** Relationship between relative air humidity (RH) and $p_{ex}p_x$ from controlled environment chamber experiments with *Lolium perenne* (closed and open squares: Lehmann *et al.*, 2017; green points: J. C. Baca Cabrera *et al.* unpublished data). For both datasets, $p_{ex}p_x$ was calculated based on Eqn 1, using $\Delta^{18}O_{leaf}$ and $\Delta^{18}O_{cellulose}$ data. The biochemical fractionation ($\epsilon_{bio}$) was computed from the temperature (T) of the chamber air according to the relationship found by Sternberg & Ellsworth (2011) for submerged aquatic plants ($\epsilon_{bio} = 0.0073T^2 - 0.4375T + 32.528$; see their Fig. 2) and yielded $\epsilon_{bio} = 26.8\%$ for the unpublished data of JCBC, RTH, JZ and HS (green points) and $\epsilon_{bio} = 25.5\%$ for the study of Lehmann *et al.* (2017) (closed squares). Open squares represent $p_{ex}p_x$ calculated by assuming $\epsilon_{bio} = 27\%$ (as reported by Lehmann *et al.*, 2017, their Table 4). RH was constant throughout day and night in the experiment of Lehmann *et al.* (2017), but differed between the dark and light period in the experiment of JCBC, RTH, JZ and HS (50%/75% and 75%/75%) (other experimental details are reported in Baca Cabrera *et al.*, 2020). The dashed line indicates the $p_{ex}p_x$ vs RH relationship used in the 'standard simulation', calculated from the relationship between model-data residuals and RH when a constant $p_{ex}p_x = 0.556$ was applied in the simulation (see Fig. 3 and Supporting Information Methods S3).

<figure><img src="image_6.png" /></figure>

**Fig. 3** Difference between predicted and observed $\Delta^{18}O_{cellulose}$ (a) in relation to relative humidity (RH), when $\Delta^{18}O_{cellulose}$ was predicted with a constant $p_{ex}p_x = 0.556$ and a temperature-dependent $\epsilon_{bio}$ (as in the 'standard simulation'), and (b) in relation to air temperature, when $\Delta^{18}O_{cellulose}$ was modelled using a constant $\epsilon_{bio} = 27\%$ and a RH-dependent $p_{ex}p_x$ (as in the 'standard simulation'). RH and air temperature represent the 400 GDD average of midday (± 3 h around noon) humidity and daily mean temperature, respectively.

## Results

### Metabolic pool turnover, carbon allocation and integration time

The turnover of the metabolic pool was validated by comparing the predicted $^{13}$C-labelling of $W_{pool}$ ($f_{new}$, the fraction of labelled C in $W_{pool}$), forced by a step-change of $\delta^{13}C_{CO2}$ in the MuSICA input data, with the labelling kinetics of total autotrophic respiration observed at the same site in May 2007 (Gamnitzer *et al.*, 2009; see their fig. 5). The predicted $f_{new}$ in $W_{pool}$ matched closely the observed fraction of labelled C in total autotrophic respiration (slope = 0.99; intercept = 0.06; $R^2$ = 0.98; $P < 0.001$; Fig. 4a).

Model predictions for the fraction of carbon allocated to shoot growth ($f_{shoot,growth}$) compared well with observations of $f_{shoot,growth}$ made by Schleip (2013) in the same pasture during May and September of 2007. The model predicted average $f_{shoot,growth}$ of 0.67 for spring and 0.54 for autumn 2007, while Schleip (2013) observed an average carbon allocation fraction to shoot growth of 0.65 (±0.05 SE) and 0.5 (±0.05 SE) over the same periods (Fig. 4b). The average allocation to aboveground biomass for all spring and summer/autumn periods 2007–2012 was 0.58 and 0.47, respectively.

To constrain the integration time of the $^{18}$O-signal in the leaf cellulose samples, we compared the $R^2$ between observed and predicted $\delta^{18}O_{cellulose}$ (Fig. 4c) for predictions of $\delta^{18}O_{cellulose}$ based on integration times of 50–600 GDD. Those calculations were made with the model in its standard parameterization (Table 1) and assumed leaf growth started on the 15 March every year. The $R^2$ between observed and predicted $\delta^{18}O_{cellulose}$ increased up to an integration time of 400 GDD ($R^2$ = 0.57) and decreased beyond that. This integration time of 400 GDD translated to time spans varying between 22 and 59 d in different periods, depending on thermal conditions (Fig. 4d) and was subsequently used as the standard integration time for all predictions of $\delta^{18}O_{cellulose}$ and $\Delta^{18}O_{cellulose}$.

### Observed variation of $\delta^{18}O_{cellulose}$ and $\Delta^{18}O_{cellulose}$

$\delta^{18}O_{cellulose}$ displayed dynamic variation within and between years, with pronounced increases and decreases in some years (2007, 2010) and lower variability in others (2008, 2011; Fig. 5). The total range of observed $\delta^{18}O_{cellulose}$ was 5.1‰, and a clear seasonal pattern was not evident (right panel, Fig. 5a). Annual mean $\delta^{18}O_{cellulose}$ did not differ significantly between the individual years, except for 2010 when the mean was 1.5‰ lower than the average of the other years. The lower $\delta^{18}O_{cellulose}$ in 2010 was linked to a more negative $\delta^{18}O_{rain}$ and lower leaf water $^{18}$O-isotopic enrichment in that year (cf. Hirl *et al.*, 2019).

The range of observed $\Delta^{18}O_{cellulose}$ was 50% greater than that of $\delta^{18}O_{cellulose}$ (compare Fig. 5a and b). Unlike $\delta^{18}O_{cellulose}$, average $\Delta^{18}O_{cellulose}$ declined distinctively during the growing season at a rate of 0.83‰ per month ($R^2$ = 0.90; $P < 0.01$). This was related to an increasing trend of $\delta^{18}O_{source}$ over the growing season (Hirl *et al.*, 2019). Overall, the observed variation
<figure><img src="image_7.png" /><figcaption>**Fig. 4** (a) Fraction of labelled carbon ($f_{new}$) in total autotrophic respiration as obtained from a ¹³C labelling kinetics study at the same experimental site in May 2007 (red points; Gamnitzer et al., 2009), and dynamics of $f_{new}$ in the metabolic pool ($W_{pool}$) induced by a step-change of δ¹³C~CO₂~ in the MuSICA input data (blue points). (b) Boxplots showing the fraction of carbon allocated to shoot growth ($f_{shoot,growth}$) as predicted by the allocation-and-growth model for spring (mid-March to mid-June) and summer/autumn (mid-June to end-October) periods of the study years 2007–2012. Lower whiskers represent the smallest $f_{shoot,growth}$ values that are less than 1.5 times the interquartile range below the 25th percentile, and upper whiskers represent the maximum $f_{shoot,growth}$ for each period. Red points indicate $f_{shoot,growth}$ as estimated by ¹³C-labelling for two 2-wk periods in May and September 2007 (Schleip, 2013), and blue points denote the model predictions for the same 2-wk periods. (c) $R²$ values for the comparison between predicted and observed δ¹⁸O~cellulose~. Model predictions were obtained using integration times between 50 and 600 growing-degree-days (GDD). The vertical dashed line indicates the average leaf lifespan observed by Schleip et al. (2013) for four co-dominant species of the same pasture investigated in this study. (d) Integration times (Δt) calculated from soil temperature and assuming a constant thermal age of 400 GDD with a base temperature of 4°C (see Eqn S8 in Supporting Information Methods S2). The blue points mark the days on which sampling occurred. It was assumed that leaf growth did not start before 15 March.</figcaption></figure>

of Δ¹⁸O~cellulose~ resembled only loosely that of δ¹⁸O~cellulose~ ($R²$ = -0.18 for the entire data set).

Δ¹⁸O~cellulose~ showed statistically significant relationships with most meteorological variables averaged over the respective integration time (Table 2; Fig. 6). The correlation of Δ¹⁸O~cellulose~ with midday RH ($r$ = -0.69) was stronger than with daily mean air temperature ($r$ = -0.43) and midday air temperature ($r$ = -0.37). Δ¹⁸O~cellulose~ was only weakly related to PAW in the rooting zone ($r$ = -0.24; $P$ = 0.05) and there were no statistically significant relationships with vapour pressure deficit (VPD) or annual precipitation (both $P$ > 0.05). Correlation analysis also indicated connections between Δ¹⁸O~cellulose~ and cumulative short-wave radiation ($r$ = 0.81) and wind speed ($r$ = 0.56). Yet, a sensitivity analysis in which the radiation input was halved or doubled demonstrated that cumulative short-wave radiation itself had only a very small effect on Δ¹⁸O~cellulose~ (Fig. S1), indicating

that the strong correlation with Δ¹⁸O~cellulose~ was indirect and arose primarily from the relationship of short-wave radiation with midday RH ($r$ = -0.63) and temperature ($r$ = 0.57) (Table S1). Sensitivity analysis also indicated that wind speed itself had a negligible effect on Δ¹⁸O~cellulose~ (Fig. S1).

δ¹⁸O~cellulose~ also had a clear relationship with RH ($r$ = -0.45). Unlike Δ¹⁸O~cellulose~, δ¹⁸O~cellulose~ was related to precipitation amount ($r$ = -0.40) and PAW ($r$ = -0.58), with the latter negatively related to δ¹⁸O~rain~ (Fig. S2a). Other relationships between δ¹⁸O~cellulose~ and meteorological variables were weak (short-wave downward radiation) or nonsignificant (daily mean or midday air temperature, VPD, windspeed) (Table 2; Fig. 6).

## Prediction of δ¹⁸O~cellulose~ and Δ¹⁸O~cellulose~

The standard model, with RH-sensitive $p_{ex}p_x$ and temperature-sensitive $ε_{bio}$, was able to reproduce with great accuracy the
<figure><img src="image_8.png" /><figcaption>**Fig. 5** Time course (a) of the oxygen isotope composition of leaf cellulose (δ¹⁸Ocellulose) and (b) of the isotopic enrichment of cellulose relative to source water (Δ¹⁸Ocellulose). Red dots, observed data; blue dots, model predictions obtained with the 'standard parameterization' with temperature-dependent εbio and RH-dependent pexpx. Observed Δ¹⁸Ocellulose was calculated from the δ¹⁸Ocellulose of the sample and average observed δ¹⁸Osource during 400 GDD before the sampling date (see Eqn S10 in Supporting Information Methods S2). (c) Time course of pexpx as estimated from midday relative humidity and averaged over the integration time (400 GDD). The horizontal dashed line indicates the value for pexpx used in the constant-pexpx simulations (pexpx = 0.556). (d) Calculated average εbio for the total substrate used in cellulose synthesis of a given leaf sample throughout the 400 GDD integration time. The horizontal dashed line shows εbio = 27‰. Average (2007–2012) monthly values of Δ¹⁸Ocellulose, δ¹⁸Ocellulose, pexpx and εbio are displayed on the right-hand side, with error bars denoting the standard deviations. Linear regression analysis indicated a significant trend for monthly mean Δ¹⁸Ocellulose (observed Δ¹⁸Ocellulose = 37.28 – 0.83 month; R² = 0.90; P < 0.01; predicted Δ¹⁸Ocellulose = 36.59 – 0.69 month; R² = 0.68; P < 0.05) and monthly mean pexpx (pexpx = 0.30 + 0.04 month; R² = 0.85; P < 0.01).</figcaption></figure>

observed seasonal dynamics of δ¹⁸Ocellulose (R² = 0.57) and Δ¹⁸Ocellulose (R² = 0.74) over the entire 6-yr-long study period (Figs 5, 7d). The model error and bias were small (Table 3), as the model was also able to capture the short-term variations. By contrast, predictions of Δ¹⁸Ocellulose made with constant pexpx and/or constant εbio degraded significantly the goodness-of-fit with observed Δ¹⁸Ocellulose (Fig. 7a-c).

Variation of midday RH at the study site, averaged over the integration time, was significant (47–73%) and implied a large range of modelled pexpx (0.37–0.77; average: 0.59), with a generally increasing trend during the growing season (Fig. 5c). Meanwhile, daily mean air temperature varied considerably at the scale of integration times (between 7 and 22°C), leading to pronounced variation in εbio (from 26 to 30%; Fig. 5d). εbio generally decreased from spring to summer and increased towards late autumn. The ability of the model to reproduce the observed relationships between Δ¹⁸Ocellulose (or δ¹⁸Ocellulose) and meteorological variables or PAW also depended on the inclusion of an RH-sensitive pexpx and a temperature-sensitive εbio (Table 2). In particular, the model was unable to reproduce the observed relationship between Δ¹⁸Ocellulose and air temperature when a constant

εbio of 27‰ was used instead of a temperature-dependent one (Fig. S3d–f).

Relationship between canopy conductance and Δ¹⁸Ocellulose or δ¹⁸Ocellulose

Observed Δ¹⁸Ocellulose was negatively related to midday canopy conductance predicted by the MuSICA model (R² = 0.26; P < 0.001; Table 2; Fig. 8), with a 100 mmol m⁻² s⁻¹ increase in gcanopy connected to a 1.4‰ decrease of Δ¹⁸Ocellulose. Again, the relationship between midday canopy conductance and observed or predicted Δ¹⁸Ocellulose was the same if the prediction was based on RH-sensitive pexpx and temperature-sensitive εbio, but not if constants for pexpx or εbio were used.

The relationship between observed δ¹⁸Ocellulose and modelled midday canopy conductance was also negative (*P* < 0.05), although the slope and *R*² for that relationship were much smaller than those for Δ¹⁸Ocellulose. The relationship between predicted δ¹⁸Ocellulose and modelled canopy conductance was similar to the observations when predictions were based on RH-sensitive pexpx and temperature-sensitive εbio, and became
<table><caption>**Table 2** Regression equations for the relationships of observed and predicted Δ¹⁸O<sub>cellulose</sub> and δ¹⁸O<sub>cellulose</sub> with meteorological variables at Grünschwage pasture paddock no. 8.</caption><thead><tr><th rowspan="2"></th><th colspan="2">Δ¹⁸O<sub>cellulose</sub></th><th colspan="2">δ¹⁸O<sub>cellulose</sub></th></tr><tr><th>Observed</th><th>Predicted</th><th>Observed</th><th>Predicted</th></tr></thead><tbody><tr><td>RH</td><td>Δ¹⁸O = 42.60 – 0.19RH;<br>R² = 0.48; P < 0.001</td><td>Δ¹⁸O = 42.42 – 0.18RH;<br>R² = 0.51; P < 0.001</td><td>δ¹⁸O = 29.31 – 0.08RH;<br>R² = 0.21; P < 0.001</td><td>δ¹⁸O = 32.22 – 0.12RH;<br>R² = 0.31; P < 0.001</td></tr><tr><td>Daily mean T<sub>air</sub></td><td>Δ¹⁸O = 34.65 – 0.21T<sub>air</sub>;<br>R² = 0.19; P < 0.001</td><td>Δ¹⁸O = 35.65 – 0.26T<sub>air</sub>;<br>R² = 0.32; P < 0.001</td><td>ns</td><td>ns</td></tr><tr><td>Midday T<sub>air</sub></td><td>Δ¹⁸O = 34.59 – 0.18T<sub>air</sub>;<br>R² = 0.14; P < 0.01</td><td>Δ¹⁸O = 35.66 – 0.22T<sub>air</sub>;<br>R² = 0.25; P < 0.001</td><td>ns</td><td>ns</td></tr><tr><td>VPD</td><td>ns</td><td>ns</td><td>ns</td><td>ns</td></tr><tr><td>PAW</td><td>Δ¹⁸O = 32.04 – 0.03PAW;<br>R² = 0.06; P = 0.0476</td><td>ns</td><td>δ¹⁸O = 25.80 – 0.04PAW;<br>R² = 0.33; P < 0.001</td><td>δ¹⁸O = 26.58 – 0.05PAW;<br>R² = 0.32; P < 0.001</td></tr><tr><td>Precip</td><td>ns</td><td>ns</td><td>δ¹⁸O = 25.26 – 0.01Rain;<br>R² = 0.16; P < 0.001</td><td>δ¹⁸O = 25.90 – 0.01 Rain;<br>R² = 0.14; P < 0.01</td></tr><tr><td>Short-wave radiation</td><td>Δ¹⁸O = 25.91 + 0.01R<sub>s↓</sub>;<br>R² = 0.65; P < 0.001</td><td>Δ¹⁸O = 25.82 + 0.01R<sub>s↓</sub>;<br>R² = 0.83; P < 0.001</td><td>δ¹⁸O = 23.38 + 0.002R<sub>s↓</sub>;<br>R² = 0.06; P = 0.046</td><td>δ¹⁸O = 23.42 + 0.003R<sub>s↓</sub>;<br>R² = 0.08; P = 0.015</td></tr><tr><td>Wind speed</td><td>Δ¹⁸O = 26.41 + 1.34u;<br>R² = 0.32; P < 0.001</td><td>Δ¹⁸O = 26.73 + 1.30u;<br>R² = 0.34; P < 0.001</td><td>ns</td><td>ns</td></tr></tbody></table>

Relative humidity (RH), midday air temperature (Midday T<sub>air</sub>), vapour pressure deficit (VPD), plant-available water (PAW) and wind speed (u) all represent midday (± 3 h around noon) values averaged over the integration time Δt (400 GDD). Daily mean T<sub>air</sub> represents daily average air temperature over Δt, and precipitation amount (Precip) and short-wave radiation (R<sub>s↓</sub>) represent the precipitation sum and the total sum of incoming short-wave radiation within Δt. ns, not significant (P > 0.05).

insignificant when predictions used constant values for $\epsilon_{bio}$, or $p_{exp}p_{s}$ and $\epsilon_{bio}$.

## Sensitivity to model parameters

Model predictions of δ¹⁸O<sub>cellulose</sub> or Δ¹⁸O<sub>cellulose</sub> were relatively insensitive to alterations of the parameters of the allocation-and-growth model (Table 1; Fig. S1), except for integration time (Fig. 4c). That is, both the mean sensitivity (i.e. the mean difference between the sensitivity run and standard run for predictions of δ¹⁸O<sub>cellulose</sub> (or Δ¹⁸O<sub>cellulose</sub>)) as well as the standard deviation of the sensitivity was smaller than 0.2‰ for each parameter value (Fig. S1).

In the MuSICA model, a 2.5-fold increase of $m_{gs}$ (see Table 1) – the slope of the Ball–Woodrow–Berry stomatal conductance model (Ball et al., 1987) – caused an average reduction of 0.84‰ of the predicted δ¹⁸O<sub>cellulose</sub> and Δ¹⁸O<sub>cellulose</sub>. For a particular situation (time), the size of that effect depended on the conditions prevailing during the respective integration time. This conditionality was reflected in the relatively high standard deviations between individual sensitivity and standard model runs for $m_{gs}$ (Fig. S1). Conversely, a reduction of $m_{gs}$ by one-third caused an average increase of 0.3‰, with the increase again dependent on prevailing conditions, as above. On the other hand, increasing $V_{cmax}$ and $J_{max}$ by 2.2-fold or reducing it by two-thirds had only small effects on the prediction of δ¹⁸O<sub>cellulose</sub> and Δ¹⁸O<sub>cellulose</sub> (mean sensitivity ≤ 0.32‰).

In general, predicted Δ¹⁸O<sub>cellulose</sub> decreased (increased) with increasing (decreasing) temperature in the sensitivity analysis (Fig. S4). If $\epsilon_{bio}$ was allowed to vary with temperature (corresponding to the default parameterization), a 1°C increase

(decrease) in temperature caused a 0.28‰ decrease (increase) in the predicted Δ¹⁸O<sub>cellulose</sub>. Conversely, if $\epsilon_{bio}$ was set to be constant (at 27‰), the resulting temperature-sensitivity of predicted Δ¹⁸O<sub>cellulose</sub> was only −0.11‰ °C⁻¹.

## Discussion

### Estimates of isotopic signal integration time in cellulose agree with leaf lifespan and residence time of nonstructural carbon

This work presents a new allocation-and-growth model that generates realistic estimates for the turnover of the metabolic pool used to supply autotrophic respiration, the allocation of assimilates to shoot and root growth, and the integration (or residence time) of cellulose in growing leaf material in a drought-prone, temperate grassland ecosystem. When coupled to a recently published version of an ¹⁸O-enabled soil–vegetation–atmosphere transfer model (MuSICA) parameterized for a grassland (Hirl et al., 2019), this allocation-and-growth model provided a faithful prediction of the fortnightly, seasonal and multi-annual variation of the ¹⁸O composition of cellulose in mixed-species leaf samples from this pasture ecosystem. The coupled model also enabled an explicit evaluation of the current theory of ¹⁸O-enrichment of cellulose (Δ¹⁸O<sub>cellulose</sub>), namely the factors that determine the relationship between δ¹⁸O<sub>cellulose</sub> and δ¹⁸O<sub>source</sub> on the one hand and those of δ¹⁸O<sub>leaf</sub> on the other. We found compelling evidence that: $\epsilon_{bio}$, the average biochemical fractionation between the organic substrate used for cellulose synthesis and water in the field, is temperature-dependent, in close agreement with studies of submerged aquatic plants as shown by
<figure><img src="image_9.png" /><figcaption>**Fig. 6** Correlation coefficients for the relationships between (a) $\Delta^{18}\text{O}_{\text{cellulose}}$ and meteorological variables and (b) $\delta^{18}\text{O}_{\text{cellulose}}$ and meteorological variables: relative humidity (RH), air temperature ($T_{\text{air}}$), vapour pressure deficit of the air (VPD), plant-available water (PAW), precipitation amount (Precip), incoming (downward) short-wave radiation ($R_{s\downarrow}$) and wind speed ($u$). Red bars, observed data; blue bars, predicted data. RH, VPD and $u$ represent midday ($\pm$ 3 h around noon) values averaged over the integration time $\Delta t$ (400 GDD); $T_{\text{air}}$ represents daily mean values averaged over $\Delta t$; and $R_{s\downarrow}$ and Precip represent the total sums of incoming short-wave radiation and the total precipitation within $\Delta t$. All predictions were made with the model in 'standard parameterization', including temperature-sensitive $\epsilon_{\text{bio}}$ and relative humidity-sensitive $p_{\text{exp}}p_x$. Asterisks indicate the significance levels: ***, $P < 0.001$; **, $P < 0.05$.</figcaption></figure>

Sternberg & Ellsworth (2011); and $p_{\text{exp}}p_x$, the proportion of oxygen in cellulose derived from source water, responded to RH in accordance with the findings of Lehmann *et al.* (2017) and our own investigations (unpublished data) with *L. perenne* in controlled environments.

To predict $\delta^{18}\text{O}_{\text{cellulose}}$ accurately, the integration time used in the model calculations was particularly important. Model-data comparison of $\delta^{18}\text{O}_{\text{cellulose}}$ indicated a best match with 400 GDD. This was 14% shorter than the average observed leaf lifespan (LLS; 463 ± 56 GDD) of the main species (*L. perenne*, *P. pratensis*, *T. officinale* and *T. repens*) at the same site (Schleip *et al.*, 2013). A possible explanation is that Schleip *et al.* considered that LLS ended when a senescing leaf had 25% chlorotic tissue while leaf sampling for the present investigation comprised

only fully green leaf blades and excluded any chlorotic leaf blades. Therefore, the collected leaves were probably not older than *c.* 320–450 GDD (compare with fig. 2 in Schleip *et al.*, 2013), in close agreement with the observed best match for an integration time of *c.* 400 GDD (Fig. 4c). This value also agrees well with the mean residence time of structural carbon in above-ground biomass of the codominant species at the same site observed by Ostler *et al.* (2016).

First field-based evidence for a strong temperature effect on $\epsilon_{\text{bio}}$, in agreement with laboratory studies

Over the integration time, air temperature ranged from 7 to 22°C and midday RH from 47 to 73%. Importantly, however,
<figure><img src="image_10.png" /><figcaption>**Fig. 7** Scatter plots showing the relationship between predicted and observed ¹⁸O-enrichment of cellulose relative to source water (Δ¹⁸Ocellulose) for predictions based on (a) εbio = 27‰ and pexpx = 0.556, (b) temperature-dependent εbio and pexpx = 0.556, (c) εbio = 27‰ and RH-dependent pexpx, and (d) temperature-dependent εbio and RH-dependent pexpx (i.e. the 'standard simulation'). Solid lines indicate the 1 : 1 line.</figcaption></figure>

<table><caption>**Table 3** R², mean bias error (MBE) and mean absolute error (MAE) for the comparison between predicted and observed δ¹⁸Ocellulose or Δ¹⁸Ocellulose at Grünschwaige pasture paddock no. 8.</caption><thead><tr><th></th><th>R<sup>2</sup></th><th>MBE</th><th>MAE</th></tr></thead><tbody><tr><td>Standard simulation</td><td></td><td></td><td></td></tr><tr><td>δ<sup>18</sup>O<sub>cellulose</sub></td><td>0.57</td><td>0.5</td><td>0.8</td></tr><tr><td>Δ<sup>18</sup>O<sub>cellulose</sub></td><td>0.74</td><td>0.2</td><td>0.6</td></tr><tr><td>Const. ε<sub>bio</sub>; const. p<sub>ex</sub>p<sub>x</sub>:</td><td></td><td></td><td></td></tr><tr><td>δ<sup>18</sup>O<sub>cellulose</sub></td><td>0.26</td><td>0</td><td>0.8</td></tr><tr><td>Δ<sup>18</sup>O<sub>cellulose</sub></td><td>0.62</td><td>-0.3</td><td>0.9</td></tr><tr><td>Var. ε<sub>bio</sub>; const. p<sub>ex</sub>p<sub>x</sub></td><td></td><td></td><td></td></tr><tr><td>δ<sup>18</sup>O<sub>cellulose</sub></td><td>0.40</td><td>0</td><td>0.8</td></tr><tr><td>Δ<sup>18</sup>O<sub>cellulose</sub></td><td>0.63</td><td>0</td><td>0.8</td></tr><tr><td>Const. ε<sub>bio</sub>; var. p<sub>ex</sub>p<sub>x</sub></td><td></td><td></td><td></td></tr><tr><td>δ<sup>18</sup>O<sub>cellulose</sub></td><td>0.49</td><td>0.2</td><td>0.8</td></tr><tr><td>Δ<sup>18</sup>O<sub>cellulose</sub></td><td>0.64</td><td>-0.2</td><td>0.8</td></tr></tbody></table>

Predictions were made with the standard parameterization of the model (Tair-dependent εbio; RH-dependent pexpx), and with constant εbio = 27‰ and constant pexpx = 0.556, Tair-dependent εbio and constant pexpx = 0.556, or constant εbio = 27‰ and RH-dependent pexpx. Constant and variable (i.e. Tair-dependent εbio or RH-dependent pexpx) parameters are coded as 'Const.' and 'Var.' in the table entries above. MBE and MAE values are given in per mil (‰). The MAE between the δ¹⁸O values of the replicate samples collected on the different dates was 0.4‰.

variations of RH and temperature were not significantly correlated at the integration time-scale (P = 0.50), meaning that RH and air temperature varied largely independently from each other. This factor aided/enabled the identification and distinction of the RH effect on pexpx and of the temperature effect on εbio.

<figure><img src="image_11.png" /><figcaption>**Fig. 8** Relationships between (a and b) Δ¹⁸Ocellulose and canopy conductance, and (c and d) δ¹⁸Ocellulose and canopy conductance. (a, c) Observed relationships, (b, d) predicted relationships obtained with the model in standard parameterization with temperature-dependent εbio and RH-dependent pexpx. Canopy conductance was modelled for midday (±3 h around noon) conditions averaged over the integration time Δt and with the model in standard parameterization (Hirl et al., 2019). Solid lines represent the linear regression lines: (a) Δ¹⁸O = 35.79 - 0.014g; R² = 0.26; P < 0.001; (b) Δ¹⁸O = 36.38 - 0.015g; R² = 0.33; P < 0.001; (c) δ¹⁸O = 26.06 - 0.005g; R² = 0.09; P = 0.017; (d) δ¹⁸O = 28.36 - 0.01g; R² = 0.25; P < 0.001.</figcaption></figure>

Notably, daily mean temperatures over the integration time covered most of the temperature-sensitive range of εbio (Sternberg & Ellsworth, 2011), explaining why the inclusion of a temperature-dependent εbio was so critical for simulating Δ¹⁸Ocellulose. Unfortunately, it is presently unknown how temperature influences the relevant biochemical mechanisms and their associated isotope effects that combine to yield the 'average biochemical fractionation between substrate for cellulose synthesis and water' εbio. In that regard, however, it is interesting and encouraging that the temperature-dependence of εbio observed here matched closely the patterns observed by Sternberg & Ellsworth (2011) in aquatic and heterotrophic systems. To the best of our knowledge, convincing general, field-based evidence supporting the requirement of a temperature-sensitive εbio has not been published so far. Still, a possible temperature-sensitivity of εbio has been discussed in modelling studies on tree-ring δ¹⁸Ocellulose by Keel et al. (2016) and Lavergne et al. (2017) on tree species from different functional groups growing across a range of temperate to cold environments. Partial evidence in favour of a temperature-sensitive εbio was presented by both groups, although overall evidence was inconclusive because of uncertainties in either the models or the climate and site data. Strong evidence for a temperature-sensitive εbio is reinforced in our comprehensive model parameterization and validation study against an extensive field dataset. In particular, the leaf water modelling, partitioning of source (δ¹⁸Osource)
and enrichment effects (Δ¹⁸Oleaf) on leaf water isotope composition (δ¹⁸Oleaf) (Hirl *et al.*, 2019) permitted a very robust modelling of Δ¹⁸Ocellulose that could be contrasted with observations of Δ¹⁸Ocellulose, across a multiyear dataset using the same set of model parameters.

Sensitivity analyses of temperature effects on predictions of Δ¹⁸Ocellulose demonstrated that c. 60% of the temperature effect in Δ¹⁸Ocellulose was related to εbio, with the remaining 40% connected to all other temperature-dependent processes influencing Δ¹⁸Ocellulose. Interestingly, the temperature sensitivity of Δ¹⁸Ocellulose (−0.28‰ ±1‰) was similar in magnitude but opposite in sign to the temperature sensitivity of δ¹⁸Orain (+0.36‰ ±1‰; Fig. S2b). This caused a lack of correlation between δ¹⁸Ocellulose and temperature, and highlights the need (and benefit) of studying both Δ¹⁸Ocellulose and δ¹⁸Ocellulose. Previous studies found a significant correlation between δ¹⁸Ocellulose (mainly from tree rings) and temperature. These studies used different temporal (decadal or century-scale changes in contrast to the seasonal patterns studied here), spatial (latitudinal or altitudinal, as compared to the stationary observations in the present study) or aridity gradients, and may have also differed in the temperature sensitivity of Δ¹⁸Ocellulose relative to that of δ¹⁸Orain (e.g. Anderson *et al.*, 1998; Saurer *et al.*, 2002; Kress *et al.*, 2010; Song *et al.*, 2011).

Evidence for an increase of $p_{ex}p_x$ with air humidity, possibly linked to leaf water $^{18}$O-enrichment along leaf blades

Model-data comparison also strongly supported the inclusion of an RH-dependent $p_{ex}p_x$ in the computation of Δ¹⁸Ocellulose. This RH dependency of $p_{ex}p_x$ was derived from the relationship between RH and the model-data residuals when Δ¹⁸Ocellulose was predicted with a constant $p_{ex}p_x$ of 0.556, combined with Eqns S7 and S9 (see Methods S2 and S3). A similar agreement between predicted and observed data was obtained when using the RH-sensitivity of $p_{ex}p_x$ observed by Lehmann *et al.* (2017) in a controlled environment study with *L. perenne* and *D. glomerata*, two of the codominant species present in our system. The RH dependency of $p_{ex}p_x$ required to link Δ¹⁸Ocellulose and Δ¹⁸Oleaf has been discussed previously for a range of C₃ and C₄ grasses (Liu *et al.*, 2016). Failure to predict Δ¹⁸Ocellulose with a constant (i.e. RH-insensitive) $p_{ex}p_x$ was not related to erroneous MuSICA predictions of Δ¹⁸Oleaf, as these exhibited a virtually identical RH-response to observed Δ¹⁸Oleaf (Hirl *et al.*, 2019). Predictions of Δ¹⁸Oassim by MuSICA were based on bulk leaf water Δ¹⁸Oleaf and the common assumption that new assimilates are in isotopic equilibrium with Δ¹⁸Oleaf (Δ¹⁸Oassim = Δ¹⁸Oleaf + εbio; Barbour, 2007). Lehmann *et al.* (2017) showed that this assumption may not always hold in grasses where RH was affecting the δ¹⁸O of sucrose (δ¹⁸Osucrose) more strongly than δ¹⁸Oleaf. These results support the view that Δ¹⁸Osucrose is not always equal to Δ¹⁸Oleaf + εbio in grasses, and that RH affects the divergence between Δ¹⁸Oleaf and the Δ¹⁸O of the water in which assimilation and sucrose synthesis takes place (Δ¹⁸O sucwater). This divergence between Δ¹⁸Oleaf and Δ¹⁸Osuc-water may be related to the gradient of ¹⁸O enrichment along leaf blades observed by Helliker & Ehleringer (2000, 2002a) and Gan *et al.* (2003), which is

particularly steep at low RH. Uncertainties on Δ¹⁸O sucwater affect the calculation of $p_{ex}p_x$. $p_x$ is commonly calculated from a two-end-member mixing model, the end-members being the Δ¹⁸O of water at the site of cellulose synthesis (Δ¹⁸Ocel-water) and Δ¹⁸O sucwater, with the latter approximated as Δ¹⁸Oleaf: $p_x = 1 - Δ¹⁸O_{cel-water}/Δ¹⁸O_{suc-water}$. A deviation between Δ¹⁸O sucwater and Δ¹⁸Oleaf affects the calculation of $p_x$. However, for grasses, this error must be small, as the water in the leaf growth and differentiation zone of grasses is close to source water (Δ¹⁸Ocel-water of c. 0) so that $p_x$ is c. 1 (Liu *et al.*, 2017a). Accordingly, the divergence between Δ¹⁸O sucwater and Δ¹⁸Oleaf noted by Lehmann *et al.* (2017) mostly affects the estimate of $p_{ex}$.

Other factors that have been related to variations of $p_{ex}$ have included ¹⁸O-exchange during phloem transport from the leaves to the growing tissue (Gessler *et al.*, 2007; but see Gessler *et al.*, 2013) and futile cycling of the growth substrate within the growing tissue (Barbour, 2007), potentially linked to cellular growth rate or other cellular anatomical features, such as the lumen area of cambial cells (Szejner *et al.*, 2020). The rate of futile cycling has been related to the turnover of the water-soluble carbohydrate pool in *Ricinus communis* (Song *et al.*, 2014). However, we could not detect a significant relationship between the modelled mean residence time of substrate in the metabolic pool ($\tau_{pool}$) and $p_{ex}$, estimated from $p_{ex}p_x$ with $p_x = 1$ (Fig. S5), although statistical noise may have been a factor. Also, modelled integration time (in days) – which is a function of leaf appearance, growth and senescence rates that are all closely coordinated in grasses (Lemaire *et al.*, 2000; Schleip *et al.*, 2013) – did not correlate with estimates of $p_{ex}$. Lastly, in a recent study, we did not observe an effect of RH on the hydraulic conductance of *L. perenne* vegetative plants in controlled environments (Baca Cabrera *et al.*, 2020), providing no (physiological) indication of an effect of RH on xylem lumen area. Clearly, there is a great need for detailed biochemical investigations of the factors underlying the variation of $p_{ex}$.

Predictions of canopy conductance from ¹⁸O-enrichment of cellulose required a temperature-dependent εbio and humidity-sensitive $p_{ex}p_x$

Finally, this work demonstrates a significant negative relationship between midday canopy conductance ($g_{canopy}$) and both Δ¹⁸Ocellulose and δ¹⁸Ocellulose. Although used in multiple studies to interpret variation in Δ¹³C and intrinsic water-use efficiency, experimental or empirical evidence for the relationship between Δ¹⁸Ocellulose (or δ¹⁸Ocellulose) and stomatal conductance is relatively scarce (Barbour *et al.*, 2000; Grams *et al.*, 2007; Sullivan & Welker, 2007; Moreno-Gutiérrez *et al.*, 2012). In principle, the correlation between $g_{canopy}$ and Δ¹⁸Ocellulose could be caused by any environmental factor that affects stomatal opening and consequently alters leaf temperature, leaf-to-air vapour pressure difference, and thus Δ¹⁸Oleaf, Δ¹⁸Osuc-water, εbio and ultimately Δ¹⁸Ocellulose. Correlations between Δ¹⁸Ocellulose and stomatal conductance observed in previous studies were evoked by treatment differences in air CO₂ and O₃ concentration and by interplant competition (Grams *et al.*, 2007), or by variation in soil temperature and soil water status (Sullivan & Welker, 2007).
In a previous study, we found a significant effect of both soil water content and RH on Δ¹⁸Oleaf, and a significant relationship between soil moisture and canopy conductance (Hirl *et al.*, 2019). Remarkably, however, we could not identify a drought-related increase of Δ¹⁸Ocellulose, which would indicate a drought-related decrease of stomatal conductance (Fig. S6). We believe that absence of a drought signal in Δ¹⁸Ocellulose is caused by the low assimilation rate and deceleration (or complete cessation) of leaf growth under drought. By contrast, both Δ¹⁸Ocellulose (Table 2; Fig. 6; Fig. S3a,c) and gcanopy (R² = 0.13; *P* < 0.01) were significantly related to RH. The RH-sensitivity of Δ¹⁸Ocellulose was even higher than that of Δ¹⁸Oleaf (−0.15‰ %⁻¹), due to the relationship between RH and pexpx (as already discussed). If Δ¹⁸O suc-water is more strongly related to evaporative conditions than Δ¹⁸Oleaf, the stomatal conductance signal in cellulose may in fact be more pronounced than previously expected solely from the climate-sensitivity of bulk leaf water. This lends further support to studies that aim to reconstruct stomatal conductance from δ¹⁸Ocellulose.

## Conclusions and perspective

This study provides strong evidence for important climate-sensitive variation of the parameters pexpx and εbio of the Barbour-Farquhar model in a terrestrial ecosystem. Elucidation of those sensitivities demanded and relied on the use of a carefully parameterized, ¹⁸O-enabled process-based soil-plant-atmosphere transfer model and the existence of a detailed multiseasonal observational data set of ¹⁸O signals in all relevant ecosystem water pools and leaf cellulose. As a result, our work demonstrates at the ecosystem scale the validity of earlier conclusions that were drawn from model-type, experimental studies conducted in steady-state, controlled environments, but have not been generally considered in the relevant fields of terrestrial ecosystem sciences. Our results have important implications for the interpretation of seasonal, interannual and geographical variations of Δ¹⁸Ocellulose and δ¹⁸Ocellulose in terms of plant physiology and climate. Existing datasets, for example on tree-ring Δ¹⁸Ocellulose or δ¹⁸Ocellulose from boreal to subtropical ecosystems, should benefit from a re-evaluation that considers the varying nature of biochemical fractionation and isotopic exchange with source and leaf water. In addition, there is a great need for more targeted studies investigating the mechanisms underlying the large observed effect of temperature on εbio and the RH-dependent variation of pexpx. Such knowledge will help us to better understand the physiological information that is imprinted in cellulose-¹⁸O signals from past and present environments.

## Acknowledgements

We thank Erna Eschenbach†, Angela Ernst-Schwärzli, Anja Schmidt, Monika Michler, Hans Vogl, Richard Wenzel and Lenka Plavcová for technical assistance, and Iris Köhler for previous discussion. JZ was supported by the China Scholarship Council. We are grateful to Xin Song and two anonymous reviewers for

constructive comments. This work was supported by the Deutsche Forschungsgemeinschaft (DFG SCHN 557/9-1).

## Author contributions

RTH, JO and HS designed the research. RTH, UO and HS designed the allocation-and-growth model. RTH analysed the data and performed the modelling with guidance by JO and UO. RS performed the isotope analysis. HS, UO and IS designed and UO and IS performed the tracer experiment. HS and RTH planned and RTH, JCBC and JZ performed the mesocosm experiment. RTH wrote the first draft. RTH, JO, UO, RS, JCBC, JZ, IS, LW and HS contributed to the discussion and the revision of the manuscript.

## ORCID

Juan C. Baca Cabrera ID https://orcid.org/0000-0001-8159-3837

Jérôme Ogée ID https://orcid.org/0000-0002-3365-8584

Ulrike Ostler ID https://orcid.org/0000-0003-4487-5805

Hans Schnyder ID https://orcid.org/0000-0002-0139-7535

Lisa Wingate ID https://orcid.org/0000-0003-1921-1556

## Data availability

The MuSICA model is written in FORTRAN 90 with scripts in PYTHON or R. The model code is currently on a private repository (https://bitbucket.org/musica_dev/musica/src/master/) accessible upon request and should very soon be moved to a public repository. The data and the R code for the allocation-and-growth model are also available upon request.

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## Supporting Information

Additional Supporting Information may be found online in the Supporting Information section at the end of the article.

**Fig. S1** Sensitivity of modelled δ¹⁸Ocellulose and Δ¹⁸Ocellulose to the parameters of the allocation-and-growth model, to the responsiveness parameter of the Ball–Woodrow–Berry stomatal conductance model (mgs; Ball *et al.*, 1987), to maximum rate of carboxylation and potential rate of electron transport (Vcmax and Jmax), and to incoming short-wave radiation and wind speed.

**Fig. S2** Relationship between the δ¹⁸O of rain collected at the Grünschwaige study site (see Hirl *et al.*, 2019) and plant-available water and air temperature.

**Fig. S3** Plot of Δ¹⁸Ocellulose vs midday mean relative humidity and daily mean air temperature.

**Fig. S4** Sensitivity of Δ¹⁸Ocellulose to air temperature, predicted based on a constant (εbio = 27‰) or temperature-sensitive biochemical fractionation.

**Fig. S5** Relationship between pex and the mean residence time of the metabolic pool (τpool,out), both averaged over the integration time (400 GDD).

**Fig. S6** Boxplots showing the effect of plant-available water on observed Δ¹⁸Ocellulose, predicted Δ¹⁸Ocellulose and modelled midday canopy conductance, gcanopy.

**Methods S1** The MuSICA model.
**Methods S2** The allocation-and-growth model.

**Methods S3** Derivation of the $p_{exp}p_x$-RH function for the standard simulation.

**Table S1** Correlation between meteorological variables.

Please note: Wiley Blackwell are not responsible for the content or functionality of any Supporting Information supplied by the authors. Any queries (other than missing material) should be directed to the *New Phytologist* Central Office.

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