Cellulose δ¹⁸O is an index of leaf-to-air vapor pressure difference (VPD) in tropical plants

Abstract

Cellulose in plants contains oxygen that derives in most cases from precipitation. Because the stable oxygen isotope composition, δ¹⁸O, of precipitation is associated with environmental conditions, cellulose δ¹⁸O should be as well. However, plant physiological models using δ¹⁸O suggest that cellulose δ¹⁸O is influenced by a complex mix of both climatic and physiological drivers. This influence complicates the interpretation of cellulose δ¹⁸O values in a paleo-context. Here, we combined empirical data analyses with mechanistic model simulations to i) quantify the impacts that the primary climatic drivers humidity (e_a) and air temperature (T_air) have on cellulose δ¹⁸O values in different tropical ecosystems and ii) determine which environmental signal is dominating cellulose δ¹⁸O values. Our results revealed that e_a and T_air equally influence cellulose δ¹⁸O values and that distinguishing which of these factors dominates the δ¹⁸O values of cellulose cannot be accomplished in the absence of additional environmental information. However, the individual impacts of e_a and T_air on the δ¹⁸O values of cellulose can be integrated into a single index of plant-experienced atmospheric vapor demand: the leaf-to-air vapor pressure difference (VPD). We found a robust relationship between VPD and cellulose δ¹⁸O values in both empirical and modeled data in all ecosystems that we investigated. Our analysis revealed therefore that δ¹⁸O values in plant cellulose can be used as a proxy for VPD in tropical ecosystems. As VPD is an essential variable that determines the biogeochemical dynamics of ecosystems, our study has applications in ecological-, climate-, or forensic-sciences.

The oxygen stable isotope ratio (δ¹⁸O) of plant cellulose has been suggested as a powerful recorder of paleoclimatic changes (1, 2). Oxygen in plant cellulose originates from the oxygen in the plant's source water, which typically derives from precipitation. As the δ¹⁸O values of precipitation are tightly correlated with climate variables such as air temperature (T_air) or the amount and geographic origin of precipitated moisture (3, 4), a simple relationship between δ¹⁸O values of precipitation and plant cellulose δ¹⁸O values has been proposed for reconstructing past climate regimes and excursions (5, 6).

This simple relationship between precipitation and cellulose δ¹⁸O values was called into question when plant scientists demonstrated that the isotope composition of leaf water (δ¹⁸O_LW), which is the primary location of carbohydrate biosynthesis, has a strong influence on cellulose δ¹⁸O values (7–9). Leaf water δ¹⁸O values are typically enriched in ¹⁸O compared with the plant's source water (δ¹⁸O_SW) because evaporative losses of water from the leaves are greater for H₂¹⁶O than for H₂¹⁸O. The evaporative enrichment of leaf water in ¹⁸O is driven by the water vapor pressure of the atmosphere (e_a), air temperature (T_air), and the isotope composition of atmospheric water vapor (δ¹⁸O_WV) (Fig. 1) (1). In addition, plant physiological characteristics such as leaf temperature (T_leaf) and rates of stomatal conductance to water vapor loss (g_s) and transpiration (E) also affect δ¹⁸O_LW (10). Because of the many climatic and physiological variables that can affect the δ¹⁸O values of leaf water, it has proved difficult to understand which environmental signals are ultimately recorded in the δ¹⁸O of plant cellulose.

Fig. 1.

Schematic illustration showing the functional relationships between the primary model variables (rounded squares) and secondary model variables (symbols within the shaded box) that influence leaf cellulose δ¹⁸O and stem cellulose δ¹⁸O in the Péclet-modified Craig–Gordon (PMCG) model. All variables containing isotope values (secondary variables as well as model outputs) are highlighted in ovals. Solid lines represent functions contained in the original PMCG model, and dotted lines indicate the functional relationships that we added to the model so that the effects of e_a, T_air, and M_source on δ¹⁸O_LC and δ¹⁸O_SC could be tested.

Studies using simple correlation analyses to “calibrate” the δ¹⁸O signal in plant cellulose have reported various relationships between plant δ¹⁸O values and key climate variables (e_a, T_air, or precipitation amount) (5, 6, 11, 12). Such simple correlation-based calibrations of plant δ¹⁸O values are, however, problematic because the resulting relationships commonly do not provide any mechanistic reasons for their existence and suffer as such from the key weakness that we have no way of knowing how robust these relationships are over time and space (13). Robust interpretations of what plant cellulose δ¹⁸O values really tell us remain therefore a challenge, compromising our ability to use cellulose δ¹⁸O values as an effective environmental proxy.

To confront and resolve these issues we present an investigation that combines empirical data analyses with mechanistic model simulations to test the sensitivity of leaf and stem cellulose δ¹⁸O values (δ¹⁸O_LC and δ¹⁸O_SC, respectively) to the three primary climatic drivers of cellulose δ¹⁸O: e_a, T_air, and the geographic origin and isotope composition of atmospheric moisture (M_source). With our modeling approach we avoid the pitfall of using only nonmechanistic calibrations of δ¹⁸O values in cellulose. Instead, we provide the much-needed mechanistic understanding of the magnitude by which variations in e_a, T_air, and M_source influence δ¹⁸O_LC and δ¹⁸O_SC and use this information to determine the environmental signal that is ultimately dominating the δ¹⁸O values of cellulose.

Our study is based on empirical data that we collected from different tropical ecosystems arrayed along a steep climatic gradient on the windward east slope of the Mauna Loa volcano on the Island of Hawaii. We selected seven sites along the gradient that differed dramatically in mean annual precipitation (750–5,880 mm), mean annual e_a (8.0–22.6 hPa), mean annual relative humidity (66–90%), mean annual T_air (9.6–22.6 °C), and mean annual global radiation (267–384 μmol·m⁻²·s⁻¹), therefore covering ecosystems that ranged from wet tropical to dry alpine (Table S1). We were able to focus our plant sampling effort on a single woody species, Metrosideros polymorpha L. (Myrtaceae) that grows in all locations along the climate gradient. We collected xylem water (which we refer to as plant source water, δ¹⁸O_SW) from all plants in midsummer (early August 2008) and midwinter (early January 2009) to determine its mean annual isotopic composition. In early August 2008 we collected leaves and stems and extracted their cellulose to determine δ¹⁸O_LC and δ¹⁸O_SC values. We collected a mixture of leaf samples that reflected all leaf ages present on a tree. Leaves of M. polymorpha develop and grow year round and persist on the tree for >1 y (14). We therefore consider the δ¹⁸O_LC of these bulk leaf samples to reflect the mean annual values of their environmental and physiological drivers. We also collected water vapor at three locations along the gradient and one additional location on the western side of the island. We determined the diurnal variability in the vapor's oxygen isotope composition for one full day at each of the four sampling locations. Finally we recorded diurnal patterns of g_s, E, bulk leaf water δ¹⁸O, and T_leaf for M. polymorpha leaves at four locations along the gradient in August 2008. Permanent climate stations positioned along the gradient provided long-term information on e_a and T_air for our analysis. A detailed description of site characteristics and of the methods used to collect samples and extract cellulose from leaves and stems and to perform the isotope analyses of water and organic samples is provided in SI Methods.

Results and Discussion

Patterns of δ¹⁸O_SW, δ¹⁸O_LC, and δ¹⁸O_SC Along the Mauna Loa Gradient.

The plant's source water δ¹⁸O values from August 2008 and January 2009 along the gradient are in close agreement with δ¹⁸O values of precipitation that were determined on the eastward slopes of the island in a previous study (15) (Fig. S1). This result indicates that the plants along the Mauna Loa gradient relied on precipitation water that had fallen in close proximity to where they grew and that no significant soil water evaporation had altered these values.

Along the gradient δ¹⁸O_SW showed a negative relationship with altitude (Fig. 2A). Precipitation on the eastern slopes of Mauna Loa typically originates from air masses that are carried from the open Pacific Ocean toward the island. When pushed upward along the slopes of Mauna Loa, water vapor condensates due to adiabatic cooling and H₂¹⁸O precipitates preferentially from these air masses. A progressive Rayleigh-type condensation process explains why precipitation or δ¹⁸O_SW becomes continuously depleted in H₂¹⁸O as air masses move along the altitudinal Mauna Loa gradient (see ref. 15 for details).

Fig. 2.

The oxygen isotope composition of xylem water (A, δ¹⁸O_SW) and plant cellulose (B, leaf cellulose, stem cellulose) along the Mauna Loa gradient. Error bars represent 1 SD, n = 5.

Within any given site along the gradient, δ¹⁸O_SW was enriched in ¹⁸O in August 2008 compared with January 2009 (Fig. 2A). A similar seasonal pattern was previously observed for precipitation along the Hawaiian mountain slopes (15, 16). Temporal fluctuations in δ¹⁸O values of precipitation have been related to variations in T_air or precipitation amount, the latter being most important in the tropics (17). However, on the Islands of Hawaii there is no evidence that a major amount effect exists (15, 16). Rather, the observed, albeit small, seasonal variability in δ¹⁸O_SW is most likely caused by seasonal variations in the atmospheric moisture sources that reach the Island of Hawaii. Whereas trade wind-generated orographic rainfall is the dominant precipitation pattern in the summer, low-pressure storm systems and cold fronts are more frequent in the winter months. Moisture typically condensates from low-pressure storm systems before it reaches the island and as a result is depleted in H₂¹⁸O compared with trade wind-generated precipitation, which is the first condensation of ocean-derived moisture that reaches the island. Seasonal differences in the precipitation sources are therefore likely to explain the seasonal variations in δ¹⁸O_SW that we observed within each site along the Mauna Loa gradient.

Along the gradient, δ¹⁸O_LC differed from δ¹⁸O_SC by 0.1–5‰. This difference is because glucose, the primary product of photosynthesis, is produced with the isotope composition of leaf water plus a known isotopic fractionation of ∼27‰ (18, 19). When biosynthetically transformed into cellulose, glucose molecules exchange a known proportion of their oxygen atoms (∼40%) with the water at the sites of cellulose synthesis (20, 21). This exchange is with leaf water for δ¹⁸O_LC but with stem water for δ¹⁸O_SC, so that when leaf water is enriched in ¹⁸O compared with stem water, leaf cellulose is also enriched in ¹⁸O compared with stem cellulose (22).

δ¹⁸O_LC and δ¹⁸O_SC showed a relationship with altitude that was opposite in direction to that of δ¹⁸O_SW with altitude (Fig. 2B). This result strongly indicates that δ¹⁸O_LC and δ¹⁸O_SC do not closely reflect the plant's source water δ¹⁸O values along the gradient. Instead, leaf water evaporative enrichment in H₂¹⁸O has a dominant influence on the final δ¹⁸O of both leaf and stem cellulose. To identify and partition which of the primary climatic and physiological variables are responsible for imparting an evaporative signal into δ¹⁸O_LC and δ¹⁸O_SC, we used a mechanistic isotope model to test in a simulation analysis how changes in mean annual e_a, T_air, and M_source affect δ¹⁸O_LC and δ¹⁸O_SC at each of the seven different sites along the Mauna Loa gradient.

Model-Simulated Effects of e_a, T_air, and M_source on δ¹⁸O_LC and δ¹⁸O_SC.

At the core of our simulation analyses was the so-called Péclet-modified Craig–Gordon (PMCG) model that we applied to simulate the effects of e_a, T_air, and M_source on δ¹⁸O_LC and δ¹⁸O_SC (Fig. 1). In the PMCG model δ¹⁸O values of plant cellulose are driven by the primary climatic variables e_a, T_air, and M_source and by the secondary variables δ¹⁸O_SW, δ¹⁸O_WV, T_leaf, g_s, and E (23–27). Under field conditions, the secondary variables respond to changes in the primary climatic variables (Fig. 1). The influences of e_a, T_air, and M_source on the secondary variables are, however, not accounted for in the PMCG model, which, in the past, has prevented realistic simulations of δ¹⁸O in plant cellulose (13). A critical task of our investigation was therefore to constrain these uncertainties by analyzing the relationships between the primary climatic drivers and the secondary model variables for our study area and to include the resulting functions into the PMCG model (Figs. S2, S3, and S4). With this adaptation of the model, we essentially reduced the input variables of the PMCG model to the primary climatic drives e_a, T_air, and M_source (Fig. 1). This reduction allowed us to realistically simulate how changes in e_a, T_air, or M_source affect δ¹⁸O_LC and δ¹⁸O_SC. Details on the relationships between primary and secondary variables that we included into the PMCG model are provided in SI Methods.

After including the functional relationships between primary and secondary variables into the PMCG model, we optimized the model with empirical data for each site along the gradient. This optimization resulted in a fit between measured and modeled ambient cellulose δ¹⁸O values of R² = 0.97 for leaf cellulose and R² = 0.91 for stem cellulose (Fig. S5). Details on the model optimization are provided in SI Methods.

To quantify the effects that changes in the primary climatic input variables have on δ¹⁸O_LC and δ¹⁸O_SC, we varied mean annual e_a in the optimized model by 1.0, 2.5, or 5.0 hPa above or below ambient conditions and calculated the resulting effects on δ¹⁸O_LC and δ¹⁸O_SC for each of the seven sites along the gradient. Similarly, we varied mean annual T_air by 1.0, 2.5, or 5.0 °C above or below ambient conditions and calculated the resulting effects on δ¹⁸O_LC and δ¹⁸O_SC for each of the seven sites along the gradient. To test how changes in the origin of atmospheric moisture (trade wind-generated orographic rainfall or low-pressure storm systems) affect δ¹⁸O_LC and δ¹⁸O_SC, we first estimated the isotopic composition of the two moisture sources that reach the different sites along the Mauna Loa gradient (Table S2). The resulting δ¹⁸O values for the two moisture sources were then used in the simulation analyses, where we tested how a 20% increase or decrease of a respective source will affect δ¹⁸O_LC and δ¹⁸O_SC.

A primary goal of our simulations was to estimate the effects of changing e_a, T_air, or M_source on δ¹⁸O_LC and δ¹⁸O_SC. δ¹⁸O_LC and δ¹⁸O_SC reflect, however, a combined influence of δ¹⁸O_SW and Δ¹⁸O_LW (Fig. 1 and Eq. 4). We therefore also show here the effects that our simulations had on δ¹⁸O_SW and the evaporative enrichment of leaf water in H₂¹⁸O above source water (Δ¹⁸O_LW), to better illustrate how changes in T_air, e_a, and M_source affect δ¹⁸O_LC and δ¹⁸O_SC.

Model simulations illustrate that mean annual δ¹⁸O_SW responds strongly to changes in e_a but that changes in T_air had only marginal effects on mean annual δ¹⁸O_SW (Fig. 3 A and B). Interestingly, the effects of changing e_a on δ¹⁸O_SW increase in magnitude at the higher elevation sites. This response is caused by the nonlinear relationship between e_a and δ¹⁸O_WV and subsequently δ¹⁸O_SW (Fig. S2A), where the slope of the relationship between e_a and δ¹⁸O_WV becomes steeper with declining T_dew (or declining humidity). As ambient e_a declines with elevation along the Mauna Loa gradient, the nonlinear relationship between e_a, δ¹⁸O_WV, and δ¹⁸O_SW consequently leads to larger responses of δ¹⁸O_SW to changes in e_a with increasing elevation. The nonlinear response of δ¹⁸O_SW carried on into the response of δ¹⁸O_LC and δ¹⁸O_SC to e_a. In particular, at the two highest-elevation sites with the lowest ambient humidity, the strong effects of e_a on δ¹⁸O_SW lead to nonlinear responses of δ¹⁸O_LC and δ¹⁸O_SC with declining humidity.

Fig. 3.

Results of model simulations where the effects of changing humidity (e_a) and air temperature (T_air) on mean annual xylem water δ¹⁸O (A and B), leaf water Δ¹⁸O (C and D), leaf cellulose δ¹⁸O (E and F), and stem cellulose δ¹⁸O (G and H) were tested for the seven sites along the Mauna Loa climatic gradient. For the analysis, we parameterized the Péclet-modified Craig–Gordon model with data that we collected along the Mauna Loa gradient. To simulate the effects of changes in e_a and T_air, ambient e_a and T_air values were varied in the model by ±1.0, ±2.5, and ±5.0 hPa e_a or by ±1, ±2.5, and ±5.0 °C. The simulations were performed for each of the seven sites along the gradient. The Δ¹⁸O and δ¹⁸O values displayed represent the deviation from ambient conditions as a result of e_a and T_air manipulations in the model. Conditions where simulated changes in e_a and T_air resulted in unrealistic environmental conditions, where for example the actual atmospheric vapor pressure exceeded the saturation vapor pressure, are not displayed (i.e., missing values).

Mean annual Δ¹⁸O_LW responded to changes in both e_a and T_air (Fig. 3 C and D). Compared with δ¹⁸O_SW, Δ¹⁸O_LW showed a more linear response to changes in e_a and T_air across the gradient. The responses of Δ¹⁸O_LW to e_a are, however, opposite in direction to the responses of δ¹⁸O_SW to e_a.

Most importantly, model simulations illustrate that δ¹⁸O_LC and δ¹⁸O_SC responded to changes in both e_a and T_air. Overall, δ¹⁸O_LC and δ¹⁸O_SC increase with declining e_a and increasing T_air. These responses are therefore in the same direction as the responses of Δ¹⁸O_LW to e_a and T_air and in the opposite direction to the responses of δ¹⁸O_SW to e_a. Although δ¹⁸O_LC and δ¹⁸O_SC are the product of both δ¹⁸O_SW and Δ¹⁸O_LW, our simulation confirms our earlier conclusion that evaporative enrichment of leaf water in H₂¹⁸O dominates the δ¹⁸O values of leaf and stem cellulose for the tropical ecosystems that we have investigated here (Fig. 2).

The model simulations illustrate that changes in the mean annual contribution of different moisture sources (M_source) had only small effects on δ¹⁸O_SW, Δ¹⁸O_LW, δ¹⁸O_LC, and δ¹⁸O_SC that ranged between ±0.8‰ and ±1.7‰ for δ¹⁸O values in leaf and stem cellulose, respectively. Given these relatively minor effects of M_source on δ¹⁸O_LC and δ¹⁸O_SC, we did not consider M_source effects in further analyses.

An important conclusion from the model simulations is that interpreting the variability of δ¹⁸O values in plant cellulose as a sole response to changes in either T_air or e_a is not possible because both e_a and T_air have a marked effect on δ¹⁸O_LC and δ¹⁸O_SC values. This conclusion has important implications for any isotope–cellulose investigation. For example, a systematic increase in δ¹⁸O values obtained from a tree ring chronology may result from increasing T_air, decreasing e_a, or both. Distinguishing which of these factors best explain the underlying variation in δ¹⁸O_LC and δ¹⁸O_SC of such samples can therefore not be accomplished in the absence of other biological and environmental data.

Relationship Between VPD and δ¹⁸O_LC and δ¹⁸O_SC.

The effects of e_a and T_air on δ¹⁸O_LC and δ¹⁸O_SC preclude the direct use of δ¹⁸O values in plant cellulose as a sole proxy for either T_air or e_a as many past investigations have done. It is important to note, however, that the effects of T_air on δ¹⁸O_LC and δ¹⁸O_SC were largely via T_leaf, which was linearly related to T_air (Fig. 1 and Fig. S3). This relationship and the directions of the individual responses of δ¹⁸O_LC and δ¹⁸O_SC to T_air or e_a indicate that the combined effects of e_a and T_air on δ¹⁸O values of plant cellulose can be integrated into a single environmental index of atmospheric water deficit for plants, the leaf-to-air vapor pressure difference (VPD). VPD describes the difference between the vapor pressure inside the leaf that depends on T_leaf and the vapor pressure in the atmosphere. VPD is a critical environmental measure of the evaporative demand by the atmosphere for water from plant leaves and has strong implications at the plant scale for ecophysiological performance and at the ecosystem scale for water and carbon cycling. Similar to δ¹⁸O values in plant cellulose, VPD increases as T_leaf increases and as e_a declines (28). Consequently, it is reasonable to suggest that δ¹⁸O_LC or δ¹⁸O_SC could act as a viable proxy for this critical environmental variable.

To test whether δ¹⁸O_LC and δ¹⁸O_SC are robust and reliable indicators of VPD across a range of environmental conditions we compared leaf and stem cellulose δ¹⁸O values to the mean annual VPD at the seven sites that we investigated along the Mauna Loa gradient. We found that δ¹⁸O_LC and δ¹⁸O_SC values reflect VPD with very high accuracy (Fig. 4). We returned to the model simulations described above to test whether the relationship between VPD and δ¹⁸O_LC and δ¹⁸O_SC is independent of whether the variation in VPD or δ¹⁸O values was caused by changes in e_a or by changes in T_air and subsequently T_leaf. We calculated VPD for each corresponding value of δ¹⁸O_LC and δ¹⁸O_SC that we simulated and then tested the relationship between VPD and δ¹⁸O_LC and δ¹⁸O_SC for each of the seven sites that we had investigated. These simulation results indicate that relationships between VPD and δ¹⁸O values in leaf and stem cellulose were independent of whether the variations in VPD or δ¹⁸O values were caused by changes in e_a or by changes in T_air, a pattern that was consistent for all sites along the Mauna Loa gradient (Fig. 5). Together, our empirical data and model simulations show therefore that δ¹⁸O values in plant cellulose are robust indicators of VPD across the range of conditions that the seven sites along the gradient represent.

Fig. 4.

The relationship between mean annual leaf-to-air vapor pressure difference (VPD) and δ¹⁸O values in (A) leaf and (B) stem cellulose for measured values across the seven sites along the Mauna Loa gradient. Error bars represent 1 SD, n = 5.

Fig. 5.

Simulated relationships between the leaf-to-air vapor pressure difference (VPD) and leaf and stem cellulose δ¹⁸O values (LC and SC, respectively) for the seven sites along the gradient. Stars indicate measured ambient values for VPD and leaf and stem cellulose δ¹⁸O values. Circles represent values that were simulated with ambient values for T_air and e_a values that deviated by ±1.0, ±2.5, and ±5.0 hPa from ambient values. Triangles represent values that were simulated with ambient values for e_a and T_air values that deviated by ±1.0, ±2.5, and ±5.0 °C from ambient values in each site.

Our findings highlight the power of using δ¹⁸O values in plant cellulose as robust and sensitive indicators of VPD. For our purposes we collected data from a set of ecosystems along a tropical climate gradient on the slopes of Mauna Loa. The ecological and geographic setting of the Mauna Loa gradient on the island of Hawaii proved ideal for our investigations as it allowed us to constrain the variability in our data yet covered a wide range of different tropical ecosystems. In particular the well-described climate system, the consistent origin of the atmospheric moisture with an isotopic composition that can be described as a function of e_a (Fig. S2), and the fact that we were able to perform our investigations on a single species proved ideal for our investigations and allowed us to rigorously test the relationship between T_air, e_a, and subsequently VPD and δ¹⁸O values in plant cellulose. With the development of the refined model presented here future investigations can and should test the generality of the results we present for different geographic and climatic regions of the globe.

Conclusions.

Using a combination of empirical data and model-based simulations we show that δ¹⁸O_LC and δ¹⁸O_SC values are sensitive to both primary climatic drivers e_a and T_air. Our research shows that distinguishing which of these variables best explains underlying variation in δ¹⁸O_LC and δ¹⁸O_SC cannot be accomplished in the absence of other biological and environmental data. This finding has important implications for paleoclimatic reconstructions of temperature or humidity using cellulose (e.g., from tree rings or cellulose-based materials contained in Neotoma middens) that are based on nonmechanistic correlational calibrations. In fact for the range of conditions we measured and modeled here we advise against such simple correlation-based approaches. Instead, our mechanistic model simulations show that the effects of e_a and T_air on δ¹⁸O values of plant cellulose can be integrated into a single environmental index of atmospheric drought: the leaf-to-air VPD. Both model simulations and empirical data reveal a strong and robust relationship between VPD and the δ¹⁸O values of plant cellulose that is consistent across all seven tropical ecosystems that we investigated. The implication for both paleoclimatic and ecosystem research is that because VPD exerts strong controls on a plant's physiological performance, it will also be a pivotal determinant of an ecosystem's carbon and water balance. Using δ¹⁸O values in plant material as a proxy for VPD has therefore an enormous potential for understanding temporal and spatial variation of one of the key environmental drivers that influences the biogeochemical dynamics of ecosystems be they past or present.

Methods

Péclet-Modified Craig–Gordon Model.

The PMCG model that we used is based on

where, Δ¹⁸O_e is the evaporative enrichment of leaf water above the plant's source water in ¹⁸O at the sites of evaporation, ε⁺ is the equilibrium fractionation between liquid water and vapor at the air–water interfaces (29), ε_k is the kinetic fractionation that occurs during water vapor diffusion from the leaf intercellular air space to the atmosphere, Δ¹⁸O_WV describes the oxygen isotope composition of water vapor in the atmosphere above source water, and e_a/e_i is the ratio of ambient to intercellular vapor pressures (23).

This original model has been expanded for bulk leaf water evaporative enrichment (Δ¹⁸O_LW) by including a Péclet effect (= L_ME/CD) that accounts for the opposing fluxes of source water entering the leaf via the transpirational stream (E) over a path length (L_M) and the opposed diffusion of isotopically enriched water away from the sites of evaporation. D is the diffusivity of H₂¹⁸O and C is the moral density of water. For our model simulations, we used a value of 30.0 mm for L_M (SI Methods) that we held constant during the simulations (30):

Leaf water isotope composition can then be calculated as

and the oxygen isotope composition of cellulose (δ¹⁸O_C) can be calculated as

where ε_wc is the fractionation between source water δ¹⁸O and the δ¹⁸O of the primary products of photosynthesis of 27‰ (8, 18, 19), p_ex is the proportion of exchangeable oxygen in cellulose formed from sucrose, and p_x is the proportion of δ¹⁸O_SW at the site of cellulose formation (31). For our calculations we assigned a value of 0.4 to p_ex (13, 32). Best fit of the models for δ¹⁸O_LC and δ¹⁸O_SC was achieved with p_x values of 1.0 for stem cellulose and p_x values between 0.80 and 0.55 for leaf cellulose. Interestingly, p_x values for leaf cellulose along the Mauna Loa gradient turned out to be tightly correlated with the specific leaf area (R² = 0.97, P < 0.001).