Seasonal variation in δ13C and δ18O of cellulose from growth rings of Pinus radiata


  • M. M. Barbour,

    Corresponding author
    1. Environmental Biology Group, Research School of Biological Sciences, Institute of Advanced Studies, Australian National University, GPO Box 475, ACT 2601, Australia and
      M. Barbour, Landcare Research, PO Box 69, ­Lincoln, Canterbury, New Zealand. Fax: + 64 3325 2418; e-mail:
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  • A. S. Walcroft,

    1. Landcare Research, Private Bag 11052, Riddet Road, Massey University, Palmerston North, New Zealand
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  • G. D. Farquhar

    1. Environmental Biology Group, Research School of Biological Sciences, Institute of Advanced Studies, Australian National University, GPO Box 475, ACT 2601, Australia and
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M. Barbour, Landcare Research, PO Box 69, ­Lincoln, Canterbury, New Zealand. Fax: + 64 3325 2418; e-mail:


Seasonal variation in δ13C and δ18O of cellulose (δ13Cc and δ18Oc) was measured within two annual rings of Pinus radiata growing at three sites in New Zealand. In general, both δ13Cc and δ18Oc increased to a peak over summer. The three sites differed markedly in annual water balance, and these differences were reflected in δ13Cc and δ18Oc. Average δ13Cc and δ18Oc from each site were positively related, so that the driest site had the most enriched cellulose. δ13Cc and δ18Oc were also related within each site, although both the slope and the closeness of fit of the relationship varied between sites. Supporting the theory, the site with the lowest average relative humidity also had the greatest change in δ18Oc‰ change in δ13Cc. Specific climatic events, such as drought or high rainfall, were recorded as a peak or a trough in enrichment, respectively. These results suggest that seasonal and between-site variation in δ13Cc and δ18Oc are driven by the interaction between variation in climatic conditions and soil water availability, and plant response to this variation.


Interest in stable isotope ratios of tree rings has mainly been in attempts to reconstruct past climates by correlating temperature (e.g. Libby et al. 1976; Gray & Thompson 1977; Wilson & Grinsted 1977) and relative humidity (e.g. Burk & Stuiver 1981; Ramesh, Bhattacharya & Gopalan 1986; Loader, Switsur & Field 1995; Switsur & Waterhouse 1998) with carbon and oxygen isotope composition of cellulose (δ13Cc and δ18Oc). Correlations have also been attempted between δ13Cc and soil moisture and rainfall (Leavitt & Long 1991; Livingston & Spittlehouse 1996; Saurer, Aellen & Siegwolf 1997). The closeness of fit of these correlations has been variable, with no correlation between stable isotope ratios and environmental parameters in some studies, whereas in others researchers found close correlations particularly when samples were collected over a wide range of climates. For example, Burk & Stuiver (1981) found δ18Oc to increase by 0·41‰ for a 1 °C rise in temperature (r2 = 0·95) in five conifer species, and Barbour, Andrews & Farquhar (2001) found slopes between δ18Oc and temperature of 0·43 and 0·24‰ for Quercus and Pinus species, respectively, from around the world. However, Ramesh et al. (1986) found no significant correlation between the same two variables in silver fir trees from India.

Theoretical understanding of variation in the carbon isotope ratio of tree rings has been available for some time (Farquhar, O’Leary & Berry 1982; Francey & Farquhar 1982). Recently a number of researchers have presented process-based interpretations of variation in δ13C of tree rings on monthly (Walcroft et al. 1997) and annual (Korol et al. 1999; Berninger et al. 2000; Arneth et al. 2002) time scales. Development of theory to understand variations in δ18O of plant material has lagged considerably behind that of δ13C. However, recent work has improved the interpretation of variation in δ18Oc (Saurer et al. 1997; Wang, Yakir & Avishai 1998; Barbour & Farquhar 2000; Barbour et al. 2000b; Roden, Lin & Ehleringer 2000). Current understanding of the processes involved in determining δ13C and δ18O of tree ring cellulose is presented in the section ‘Isotope theory’.

A number of authors (Farquhar, Condon & Masle 1994; Yakir & Israeli 1995; Saurer et al. 1997; Barbour & Farquhar 2000; Scheidegger et al. 2000) have pointed out that simultaneous measurement of both δ13C and δ18O in plant material may be particularly useful, as external factors influence both ratios. Saurer et al. (1997) and Barbour & Farquhar (2000) suggest that the relative responses of both δ13C and δ18O can be related to the sensitivity of a plant to evaporative conditions. This hypothesis will be developed further in this paper, by incorporating recent developments in the interpretation of δ18Oc and comparing isotope ratios from tree ring cellulose from the same species at three sites differing markedly in both atmospheric and soil water ­deficits.

The plant material

Walcroft et al. (1997) recently presented data showing within-season variation in δ13C of wood from Pinus radiata trees grown at two sites in New Zealand. The trees sampled by Walcroft et al. and again in this paper are particularly well suited to studies of the relationship between climate and stable isotope compositions of their cellulose for a number of reasons. Pinus radiata grown in New Zealand forms very wide growth rings, particularly in the warmer North Island, where trees have been shown to increase in diameter throughout the year (Tennent 1986). In contrast to some tropical species, a distinct band of early wood is formed each season in P. radiata, allowing separation of annual growth rings. Early wood production in Pinus species is known to depend almost entirely on current photosynthate (e.g. Pinus resinosa, Dickmann & Kozlowski 1970; Pinus banksiana, Glerum 1980), so that cellulose laid down in spring will reflect current conditions. In contrast, deciduous species rely on stored carbohydrates for very early season xylem development (e.g. Quercus alba; Dougherty et al. 1979). The wide rings found in P. radiata grown in New Zealand allow division of each annual ring into samples representing relatively short time intervals. The limited use of stored carbohydrate for xylem formation means that the isotope composition of wood within a ring should relate fairly closely to leaf gas exchange at the time of formation, throughout the year.

Lignin is known to be deposited in xylem cell walls towards the end of the growth period of the cell (Kozlowski 1992), suggesting that photosynthate used to produce lignin may have been fixed considerably later than the photosynthate used to produce the cellulose in the same cell. Variation in the lignin content across annual rings may further complicate the isotopic signal (Walcroft et al. 1997). With these issues in mind, cellulose was extracted from the wood samples to reduce the time period over which sampled tissue was formed and to avoid differences in δ13C and δ18O between substances formed by different metabolic pathways.

In this paper we describe isotope ratios of cellulose from the same rings as studied by Walcroft et al. (1997), but increase the resolution so that each sample represents between three (over the summer period) and 30 (over the winter period) days. A tree from a third site with a climate intermediate between the sites previously investigated is also included.

Isotope theory

Isotope values are expressed as deviations (δ, ‰) from standards; PDB (fossil belemnite of the Pee Dee formation) for 13C/12C, and VSMOW (Vienna Standard Mean Oceanic Water) for 18O/16O; such that:


where R is the 13C/12C or 18O/16O ratio in the sample or the standard.

Carbon isotope theory

A simple expression relating δ13C of whole leaf tissue (δ13Cp) to δ13C of CO2 in the atmosphere (δ13Ca = −7·8‰) and the ratio of the concentration of CO2 inside the leaf (ci) and in the ambient air (ca) was presented by Farquhar et al. (1982) and Farquhar, Ehleringer & Hubick (1989):

δ13Cp  =  δ13Ca  −  a  −  (b  −  a)ci/ca,(2)

where a is the fractionation associated with diffusion of CO2 through the stomata (4·4‰) and b is the effective discrimination against 13C by ribulose biphosphate carboxylase-oxygenase (Rubisco) during carbon fixation (about 27‰). Equation 2, in the strictest sense, relates only to the products first formed by photosynthesis. Other fractionations are known to occur during further metabolism, for example, cellulose is heavier than triose phosphates (Gleixner et al. 1993) and stem cellulose is known to be heavier than leaf cellulose (Leavitt & Long 1982). Such fractionations result in tree ring cellulose having somewhat higher (2–5‰) δ13C values than the first products of photosynthesis, so that the carbon isotope composition of cellulose is given by:

δ13Cc  =  δ13Ca  −  a  −  (b  −  a)ci/ca  +  ɛpc,(3)

where ɛpc is the difference between δ13Cc and δ13Cp.

Using a leaf level process-based model combining stomatal conductance to water vapour (gs) and assimilation rate (A), and a soil water balance model, to predict average daily ci for P. radiata trees at two sites, Walcroft et al. (1997) were able to show generally good agreement between modelled ci and that estimated from Eqn 3. Variation in δ13C of wood was shown to be driven by the site-specific and seasonal variations in the interaction between micometeorological parameters and soil water availability. Variation in δ13C of cellulose is expected to follow patterns similar to those found in whole wood δ13C (Wilson & Grinsted 1977; Leavitt & Long 1982; Barbour et al. 2001).

Oxygen isotope theory

Theory has been presented to describe the enrichment of water at the sites of evaporation (δ18Oe, when compared to VSMOW, or Δ18Oe when compared to source water) in terms of fractionations and the ratio of vapour pressure in the air (ea) and inside the leaf (ei) by (Craig & Gordon 1965; Dongmann et al. 1974; Farquhar & Lloyd 1993):

δ18Oe  =  δ18Os  +  ɛ*  +  ɛk  +  (δ18Ov  −  δ18Os  −  ɛk)ea/ei,(4)

where ɛk is the kinetic fractionation factor of H218O as it diffuses through the leaf boundary layer and the stomata, ɛ* is the proportional depression of equilibrium vapour pressure by the heavier H218O (9·5 at 20 °C and 9·1 at 25 °C) and δ18Os and δ18Ov are the isotopic compositions of source water and of water vapour in the air, respectively. The oxygen isotope ratio of cellulose (δ18Oc) is known to reflect the water in which it formed due to exchange of carbonyl oxygen in organic molecules with water (Sternberg DeNiro & Savidge 1986), with an enrichment of 27‰. Saurer et al. (1997) used a simple expression to interpret variation in δ18O in stem cellulose from three tree species. This expression included a ‘dampening factor’ (f  ) to summarize the effects of leaf water isotopic heterogeneity and the exchange of oxygen atoms with stem water during cellulose synthesis from sucrose (i.e. full dampening when f = 0). The expression was then (Saurer et al. 1997):

δ18Oc  =  δ18Os  +  f [ɛk  +  ɛ*  +  (δ18Ov  −  δ18Os  −  ɛk)ea/ei]  +  ɛwc,(5)

where ɛwc is the fractionation associated with exchange between carbonyl oxygen and water (27‰).

Equation 5 is similar to that presented by Roden et al. (2000; and also see Roden & Ehleringer 1999a, b, 2000), in that a dampening factor (f0 in their case, and found to be 0·42) is used to describe the exchange of oxygen atoms with water during cellulose synthesis. However, the Roden et al. model ignores evidence in the literature of variation in f0, and of leaf water isotopic heterogenity impacting on oxygen isotope ratios (e.g. Wang et al. 1998; Barbour et al. 2000b; Barbour & Farquhar 2000).

A better understanding of the processes involved in determining the effect summarized by f (or f0) is available. Isotopic inhomogeneity in leaf water has been suggested to be a function of back diffusion of enrichment from the sites of evaporation being opposed by convection of source water to those sites via transpiration (Farquhar & Lloyd 1993; Flanagan et al. 1994; Barbour et al. 2000b). The average enrichment of leaf water above that of source water (Δ18OL ≈ δ18OL − δ18Os, where δ18OL is the isotopic composition of leaf water relative to VSMOW) over an effective length L(in m) is described by (Farquhar & Lloyd 1993):


where is the Péclet number, describing the ratio of convection to diffusion of enrichment. The Péclet number is given by:

  =  EL/(CD),(7)

where E is the evaporation rate, C is the concentration of water (55·5 × 103 mol m−3) and D is the diffusivity of H218O in water (2·66 × 10−9 m2 s−1). Sucrose formed in the photosynthesizing leaf is expected to be in isotopic equilibrium with cytoplasmic water, which we assume is close to Δ18OL (Barbour et al. 2000b).

Sucrose is loaded into the phloem and transported to the meristematic regions, including the stem. During cellulose synthesis from sucrose, oxygen atoms are able to re-exchange with water in the developing cell. Two of the 10 oxygen atoms in cellulose pass through carbonyl groups as sucrose is cleaved to form hexose phosphates. Hill et al. (1995) reported further exchange of oxygen as a result of a futile cycling of hexose phosphates through triose phosphates. The proportion of hexose phosphates involved in recycling (pex) has been found to vary between tissues (e.g. 0·47 in carrot: Sternberg et al. 1986 and 0·38 in Lemna gibba: Yakir & DeNiro 1990). In the only study on a tree species to date, recalculation of 14C label randomization data from oak presented by Hill et al. (1995) shows pex to be between 0·44 and 0·5 (Barbour & Farquhar 2000). The oxygen isotope enrichment of cellulose above source water (Δ18Oc) may be expressed (Barbour & Farquhar 2000):

Δ18Oc  =  Δ18OL(1  −  pex px)  +  ɛwc,(8)

where px is the proportion of water in the developing cell that has come from the xylem, and is therefore at δ18Os. In tree stem tissue we expect water in the developing cell to be unaffected by enrichment in the leaves because the distance between the leaf and this region is large, allowing exchange between the phloem and xylem water (Yakir 1998; L. Cernusak, personal comm.). That is, px = 1.

Equations 4 and 5 suggest that δ18Os should strongly influence δ18Oe and δ18Oc. These predicted relationships have been clearly demonstrated in a number of tree species (Roden & Ehleringer 1999a, b). Large seasonal variation in the stable isotope composition (both oxygen and hydrogen, δD) of water taken up by a plant can occur as a result of seasonal variation in δ18O and δD of rainfall, or because plants use water at differing soil depths (Dawson 1993; Dawson & Pate 1996). Such seasonal variation in isotope composition of source water is common at high latitude sites, where seasonal temperature ranges are large (IAEA 1992), and at sites where deep ground water is accessed. Evaporative enrichment of soil water near the surface is known to be particularly pronounced at sites with dry soils and low atmospheric humidity (Barnes & Allison 1983; Allison, Barnes & Hughes 1983; Allison & Hughes 1983), but in most cases the water content of the upper soil layer is too low for plant uptake, so that the extremes of surface enrichment are commonly ignored by plants (Yakir 1998). Seasonal variation in δ18O of rainfall is known to be rather small (between 2·4 and 3·8‰) at low altitude sites in New Zealand (Taylor 1990; IAEA 1992) compared with high altitude or high latitude sites. The deep soil profile at the Kawerau site was generally quite wet, so that seasonal variation in δ18O of soil water is expected to be small (Barbour 1999). Seasonal variation in soil water δ18O may be a little larger (up to 4‰Barbour 1999) at the Balmoral site, due to expected variation in δ18O of rainfall (a seasonal range of 3·8‰ is found at nearby Christchurch; Taylor 1990), and because surface evaporative enrichment is likely to occur when soil water deficits and vapour pressure deficits are high in the summer months (see Fig. 3e).

Figure 3.

Variation in climatic parameters and in δ13C and δ18O of cellulose for the tree at Balmoral. (a) Monthly rainfall and long-term average monthly rainfall (*); (b) average daily maximum temperature; (c) average vapour pressure deficit; (d) average soil water deficit; (e) δ13Cc; and (f) δ18Oc during the period that each sample represents. In (d) the dashed line represents the mid-point between field capacity (0 SWD) and the permanent wilting point of the soil.

Early research by Wilson & Grinsted (1978) showed that δ18O of tree ring cellulose varied across a growth season. Cellulose laid down in spring in Pinus radiata stems was about 2·3‰ more enriched than that formed in the winter. More recently, Hill et al. (1995) found that cellulose from early wood of oak was 1–2‰ less enriched than cellulose from late wood. Seasonal variation in δ18O of cellulose could be a result of either ea/ei decreasing as relative humidities decreased during summer, or source water δ18O increasing during the season as summer temperatures increased, or of a combination of these two processes occurring. It is expected that δ18O of tree ring cellulose will vary throughout the growing season, and that the extent of enrichment will reflect both variation in δ18Os and changes in leaf water enrichment as a result of seasonal climatic patterns and leaf-level processes.

Model predictions

Theory and models described above are combined with a simple model of photosynthesis (photosynthesis is Rubisco-limited only) to predict δ18O and δ18C with changing vapour pressure deficit (VPD), stomatal conductance (gs) and photosynthetic capacity (Vcmax). A full description of the model is given in Appendix A. To simplify the interpretation of model predictions, we first assume that δ18Os is constant throughout the growing period. With this assumption, the model predicts that changes in VPD alone will result in large variation in δ18Oc, but much smaller variation in δ13Cc (see Fig. 1a & d). Conversely, variation in the Vcmax of the leaves (varied between 24 and 34 µmol m−2 s−1, on a total leaf area basis) is expected to be reflected in δ13Cc (through changes in ci, with all other parameters remaining constant), but not in δ18Oc (see Fig. 1c & f). There should be no relationship between δ18Oc and δ13Cc if Vcmax alone changes.

Figure 1.

The modelled variation in δ13C and δ18O of cellulose when: (a) and (d) vapour pressure deficit varies; (b) and (e) stomatal conductance varies; (c) and (f) photosynthetic capacity varies. The δ13Cc and δ18Oc models used are described in Appendix A. Air temperature was kept constant at 20 °C, and stomatal conductance (gs) was varied between 0·02 and 0·48 mol m−2 s−1. Photosynthetic capacity (Vcmax) at the given temperature was varied between 24 and 34 µmol m−2 s−1. Default values used were: VPD = 0·94 kPa, gs = 0·19 mol m−2 s−1 (on a projected leaf area basis) and Vcmax = 30 µmol m−2 s−1. Source water δ18O was assumed to be constant at −8·0‰.

The models predict that both δ13Cc and δ18Oc will vary if gs changes and all other parameters remain constant (see Fig. 1b & e). However, at the range in gs expected for Pinus radiata (0·02–0·48 mol m−2 s−1, on a total leaf area basis; Sheriff & Mattay 1995), and assuming the leaves to be strongly coupled to the air (Walcroft et al. 1997), the response of δ18Oc to changes in gs is rather small. As both δ18Oc and δ13Cc are expected to be negatively related to gs, a positive relationship between the two is expected at constant VPD. An interesting point to note is that the δ18Oc response to gs is expected to be much stronger if the leaf is less coupled to the environment, such as a broad-leaf tree. This is because leaf temperature will vary with gs, which affects ei and ɛ* in Eqn 4. Appendix B gives example predictions of the model for Prunus persica, a tree with larger leaves.

The story becomes more complicated for Pinus radiata when both gs and VPD vary. Unlike ca, which is rather constant throughout the year in the Southern Hemisphere, ea can vary considerably over a season. As modelled in Eqn 4, the vapour pressure of ambient air is expected to be reflected in leaf water δ18O, and passed on to some extent to cellulose δ18O. The predicted slope of the δ18Oc : δ13Cc relationship is expected to vary with VPD (Barbour & Farquhar 2000; Scheidegger et al. 2000) if gs drives changes in isotope ratios. The slope increases with increasing VPD (see Fig. 2).

Figure 2.

The modelled relationships between vapour pressure deficit (VPD) and the ratio of variation in δ18Oc and δ13Cc when variation in δ13Cc is driven by changes in gs alone (——), or by large changes in both gs and Vcmax (– − – –), or by small variation in gs and large variation in Vcmax (- - - - -). Source water δ18O was assumed to be constant at −8·0‰. See Appendix A for details.

The slope of the δ18Oc : δ13Cc relationship is also predicted to increase with increasing VPD if both gs and Vcmax vary in the same direction over physiologically reasonable ranges. The modelled values of the slope of the δ18Oc : δ13Cc relationship when both gs and Vcmax vary are similar to those predicted when gs alone varies (see Fig. 2).

However, if gs changes only a little and Vcmax varies dramatically (again, both in the same direction), then the predicted slope of the δ18Oc : δ13Cc relationship is much greater than if gs alone varied, or if gs and Vcmax varied to the same extent (0·60‰ ‰−1 at 0·94 kPa VPD compared to 0·05‰ ‰−1). Figures 1 and 2 show that an increase in VPD not only increases δ18O of cellulose, but also increases the ratio of changes in δ18Oc and δ13Cc. It can be imagined that over a season the δ18Oc : δ13Cc relationship moves from a shallow slope with low δ18Oc in the cool, low VPD spring to a higher δ18Oc with a steeper δ18Oc/δ13Cc slope during mid-summer.

In Figs 1 and 2 the δ18O of source water is held constant. In the field δ18Oc will vary with variation in δ18Os during a season. For the tropics, which dominate global productivity, seasonal variation in δ18Os is often low. However, we recognize that the seasonal variation at our sites, discussed earlier, will sometimes be significant and confound interpretation of changes in the isotopic composition of cellulose. This means that actual values of the relationship between δ18Oc and δ13Cc from field-grown trees in this study can not be directly compared with those produced by the model.

Thus, for a single species at any one site the relationship between δ18Oc and δ13Cc can be expected to reflect a number of interacting factors. These include: seasonal variation in δ18Os, seasonal variation in VPD, severity and duration of soil water deficit, the coincidence of atmospheric and soil water deficits and plant responses to these factors. We anticipate a positive correlation between δ13Cc and δ18Oc, but that the slope of the relationship will vary between sites depending on the factors outlined above.

Materials and methods

Site description

Three sites were chosen to represent three different growth environments. Balmoral forest is situated in the South Island of New Zealand (42·52° S, 172·45° E) with low annual rainfall and wide temperature extremes. The soil at the Balmoral site is a stony silt loam with a rooting zone down to 1 m. The second site, Matangi, is just outside Hamilton, in the centre of the North Island (37·50° S, 175·18° E). It receives high annual rainfall, and has mild temperatures. The soil at Matangi is a silty loam, with an assumed rooting depth of 1 m. Kawerau is also in the North Island (38·10° S, 176·40° E) and has very high annual rainfall spread evenly throughout the year, and warm temperatures. The rooting depth at Kawerau is assumed to be 3 m (Walcroft et al. 1997), as the soil is a deep pumiceous tephra.

Climatic variables

Nearby weather stations maintained by the New Zealand Meteorological Service provided climatic variables used in a soil water model (described below): daily maximum and minimum temperatures, daily total short wave irradiance and daily total rainfall. The average daily saturation deficit was calculated from estimated daily temperature [estimated daily temperature = (2 × maximum temperature + minimum temperature)/3] and by assuming that the dew point temperature was equal to the daily minimum temperature. Monthly VPD measurements at 0900 h from two nearby weather stations were strongly correlated to calculated VPD at Balmoral (r2 = 0·73 between Culverden and Balmoral, and r2 = 0·76 between Hawarden and Balmoral), validating the method of VPD estimation. Diurnal courses of climatic variables (used in the model of evaporation) were calculated from the daily values using the procedure of Goudriaan & van Laar (1994).

Soil water balance model

The soil water balance was modelled as described in Walcroft et al. (1997) with estimates of the depth and water-holding characteristics of the Matangi soil taken from Gradwell (1968). Briefly, the root zone soil water storage (W) on the ith day was modelled by:

Wi  =  Wi − 1  +  Pi  −  Eti  −  Eui  −  Fi,(9)

where P is net precipitation, Et is evaporation from the canopy, Eu is evaporation from understorey vegetation and the forest floor, and F is drainage from the root zone. Et and Eu were modelled as described in Walcroft et al. (1997). Surface runoff was assumed to be zero as all sites were flat and well-drained. Soil water deficit was calculated by subtracting the root zone soil water on the ith day from the maximum soil water storage at the site. This soil water balance was not extended to include the isotopic composition of water, because of large uncertainties in modelling δ18O of rain, movement and mixing of rainfall events through the soil profile and evaporative enrichment from the soil surface.

Sampling procedure

A narrow block of wood encompassing two consecutive growth rings was separated from the north-facing side of a disc cut from each of three trees. The two annual rings represent growth from the southern hemisphere winter of the first season to the winter 2 years later. A sliding microtome (R Jung, Heidelberg, Germany) was used to cut each pair of rings into 240 µm slices. The rings from the Balmoral tree covered the 1993–95 seasons, when the tree was 7–8 years old. The rings sampled from the tree at the Kawerau site covered the 1991–93 seasons, when the tree was between 3 and 4 years old. The tree from the Matangi site was a mature tree in a hedgerow, and the rings were laid down during the 1987–89 seasons. Each slice was treated as a separate sample, so that the time period represented by each sample varied from 3 to 30 d, depending on the growth rate.

Cellulose extraction

Wood shavings were cut into small slivers and placed into labelled glass pipette tips between silica wool. These were then placed in a cradle (to hold the pipettes upright) within a soxhlet extraction vessel and solvent extraction carried out, first with 3 : 1 chloroform/ethanol, then pure ethanol and finally distilled water, and allowed to reflux until the solution ran clear. The samples were then placed in an ultrasonic  bath  (Loader  et al.  1997)  within  a  water-­jacketed beaker to maintain the acidified sodium chlorite bleach solution at 70 °C. The bleaching solution was replaced three times a day, with samples taking approximately 3 d to bleach to pure white. The bleached samples were then rinsed thoroughly in distilled water and placed in a 10% NaOH solution at 70 °C for 5 h to remove ­hemicellulose.

Stable isotope analysis

Extracted cellulose was dried and weighed into tin capsules for stable isotope analysis. Oxygen isotope analysis used 1 mg of cellulose whereas carbon analysis used 1·5 mg. Analysis for both isotopes was therefore possible from each sample, with the exception of three samples that required mixing with the neighbouring sample before carbon isotope analysis.

For carbon isotope analysis, samples were combusted to CO2 in a Carlo-Erba elemental analyser, then introduced into a mass spectrometer (Micromass Isochrom; VG Isotech, Middlewich, UK). A standard of beet sucrose (δ13C = −24·6‰ PDB) was used throughout the analytical runs. For oxygen isotope analysis, samples were pyrolysed to CO in a Carlo-Erba elemental analyser, then passed into a different Micromass Isochrom mass spectrometer for 18O/16O analysis, following the ­procedure described by Farquhar, Henry & Styles (1997). The  same  beet  standard  (δ18O = 30·8‰ VSMOW)  was used.

Estimating growth rate

Dendrometer bands were placed on four trees in the Balmoral forest in the spring of 1994 (Walcroft et al. 2002), allowing accurate dating of samples for the 1994–95 season at this site. The 1993–94 season was assumed to have a similar pattern of growth as the measured year.

Timing of samples from the Kawerau and Matangi sites was estimated from a sigmoidal growth curve fitted to stem increment data from P. radiata in mesic sites in the North Island of New Zealand (Jackson, Gifford & Chittenden 1976; Tennent 1986). The model was of the form:


where t is the first day (in number of days since 1 July) of the time period that the sample relates to, sample no. is the number of the sample for the season starting 1 July, and xc, c and d are fitted parameters. For example, for the 1989–90 season at Matangi, with 44 samples, xc = 220, c= 48·5 and d= 0·018, so that the time period relating to sample number 21 starts on the 205th and finishes on the 209th day after 1 July (21–25 January 1990).

Estimating average annual δ18O of rain

Annual mean δ18O of precipitation (δ18OR), weighted by rainfall amount, from five sites throughout New Zealand was used to model δ18OR at each of the experimental sites. There are two International Atomic Energy Agency (IAEA) measurement sites in New Zealand, one at Kaitaia and the other at Invercargill. Long-term δ18OR values are presented in IAEA (1992). Further data from New Zealand sites are presented by Taylor (1990), who reports δ18OR for Taupo, Lower Hutt and Christchurch. The details from all five sites are presented in Table 1. A multiple regression of δ18OR (‰) against elevation (Ev, in m), mean annual temperature (T, in °C) and mean annual precipitation (Pa, in m) produced the fit;

Table 1.  Site description, mean annual temperature and rainfall, and weighted annual average δ18O of rainfall (measured: meas., and modelled: mod.) from Eqn 11, for sampling stations. Included are standard deviations of the mean annual δ18O of rainfall [SD], number of years over which the weather and δ18OR data are averaged (weather n and isotope n, respectively), and the reference from which weather and isotope data were extracted (weather ref. and isotope ref., respectively)
SiteLatitude°SLongitude°EAltitude(m)Air temp.(°C)Rainfall(m)δ18OR meas.(‰) [SD]δ18OR mod(‰)Weather(n)Isotope(n)Weatherref.Isotope ref.
Kaitaia35·08173·168515·61·382−5·01 [0·42]−5·122626IAEA (1992)IAEA (1992)
Taupo38·72176·0840712·01·178−7·20 [0·66]−7·273211NZ Met. 1983Taylor (1990)
Lower Hutt41·23174·923412·61·394−5·80 [0·54]−5·8123 8NZ Met. 1983Taylor (1990)
Christchurch43·48172·533011·60·648−7·42 [1·04]−7·4537 5NZ Met. 1983Taylor (1990)
Invercargill46·42168·32 2 9·81·037−7·11 [0·23]−7·192626IAEA (1992)IAEA (1992)
δ18OR  =  0·29T  +  1·82Pa  −  0·0024Ev  −  11·9,(11)

with an r2 of 0·999. Equation 11 predicts δ18OR of −8·1‰ at Balmoral, −5·5‰ at Matangi and −4·5‰ at Kawerau.


Environmental conditions

Balmoral had the lowest rainfall of the three sites (1·287 m over the two seasons), and generally had the lowest temperatures, although summer maxima were more extreme than at the other sites. Balmoral also experienced the highest vapour pressure deficit (VPD) of the three sites. Winter and early spring of 1993 had lower than average rainfall at Balmoral (days 1–60, Fig. 3). However, this was followed by an extremely wet early summer, with about three times the average rainfall in December (Fig. 3, marked ‘1’). The high rainfall during this period also resulted in a reduction in the solar radiation, maximum temperature and VPD. March and April of 1994 were drier than average with rather high VPD and very low soil water levels (Fig. 3, marked ‘2’). August of 1994 was drier than average, resulting in a reduction in soil water storage, but spring and early summer received about average rainfall. December of 1994 was another very dry month, and March, April and May all had low rainfall (Fig. 3, marked ‘3’). The extended period of low rainfall, coupled with high temperatures and VPD, produced the most extreme soil water deficit during the two seasons.

Matangi generally fitted between the other sites, with nearly double the rainfall of Balmoral and 0·479 m less than Kawerau, and totalling 2·255 m over the two seasons. Average temperatures also lay between the other sites, although summer maxima tended to be less than at the other sites. VPD was generally lower at Matangi than at the other sites. January of 1988 was very dry at the Matangi site (Fig. 4), with high VPD resulting in severe reduction in soil water (Fig. 4, marked ‘1’). Such a combination of low rainfall and high VPD is very unusual for this region, and represents a severe stress for plants. April of 1988 also had well below average rainfall but did not coincide with high VPD, and soil water levels were not as severely reduced as during January (Fig. 4, marked ‘2’). The spring and early summer of 1988 were wetter than average and soil water levels were restored. February, March and April of 1989 were drier than average months for the site and soil water levels were again depleted. However, in contrast to the drought of the previous summer, maximum temperatures and VPD were not as high, so that plants should not have been as stressed (Fig. 4, marked ‘3’).

Figure 4.

Variation in climatic parameters and in δ13C and δ18O of cellulose for the tree at Matangi. (a) to (f) as for Fig. 3.

Kawerau was the wettest of the three sites, with 2·764 m falling over the two seasons. Temperatures were generally warmest at this site, but summer maxima tended to be slightly below the extremes at Balmoral. The spring of 1992 was wetter than average at Kawerau (Fig. 5), followed by lower than average rainfall during the rest of the year. Soil water was slowly depleted over this period, but did not reach levels that caused plant stress (Walcroft et al. 1997). The spring and early summer of 1993 was also wetter than average, but January 1994 was rather dry, with high VPD and daily maximum temperatures (marked with an arrow). This caused a rapid depletion of soil water which only fully recovered in June 1994. Despite the extremely low rainfall and high VPD, modelled soil water levels were not severely depleted, and were not expected to cause plant stress.

Figure 5.

Variation in climatic parameters and in δ13C and δ18O of cellulose for the tree at Kawerau. (a) to (f) as for Fig. 3.

Variation in δ13Cc

A seasonal pattern of increasing 13C of tree ring cellulose to a peak in summer was found for all three sites, as reported for wood (Walcroft et al. 1997). Balmoral had the most enriched δ13Cc, with an average of −24·4‰ compared to −25·9 at Matangi and −27·0 at Kawerau. The greatest variation in δ13Cc over the two seasons was found at the Matangi site, where δ13C ranged from −22·3 to −28·2; nearly 6‰. This compared to a seasonal variation of 5·2‰ at Balmoral and 4·1‰ at Kawerau.

The δ13C of cellulose in tree rings from the Balmoral site had a small peak in late spring of 1993, followed by a depletion over midsummer (Fig. 3, marked ‘1’). δ13Cc increased sharply to a peak enrichment of −21·7‰ in late summer (Fig. 3, marked ‘2’) then dropped to a winter low of about −26‰. δ13Cc increased again the following season, but rather than having a midsummer depression, it increased steadily to a broad midsummer maximum (Fig. 3, marked ‘3’), and dropped steadily in autumn to a midwinter minimum in June 1995. Table 2 shows that δ13Cc was significantly (P < 0·0001) positively related to both VPD and SWD.

Table 2.  Correlation coefficients for the relationships between isotope ratios of tree ring cellulose, and vapour pressure deficit (VPD) and soil water deficit (SWD)
  • NS

    P > 0·10;

  • *

    P < 0·01;

  • **

    P < 0·001;

  • ***

    P < 0·0001.


The tree from Matangi showed a steady increase in δ13Cc during spring and early summer, followed by a very sharp peak during January 1988 (Fig. 4, marked ‘1’). The second season had a broad peak in midsummer, about 3‰ lower than the peak in the previous season. δ13Cc for the Matangi samples was significantly (P < 0·0001) positively related to VPD, but showed no significant correlation with SWD (see Table 2).

Cellulose from the tree at Kawerau showed a clear seasonal pattern in δ13C during the warmer summer months (Fig. 5). During the first season δ13Cc increased steadily during spring and early summer to a peak of −25‰ in midsummer, followed by a steady decrease to a midwinter low of −28·5‰. The following season δ13Cc increased in enrichment until spring, when it levelled off and stayed constant at about −27‰ until late summer when there was a sharp peak in enrichment (Fig. 5, marked with an arrow). Like the samples from Balmoral, δ13Cc was significantly positively correlated to both VPD and SWL (P < 0·0001 and P < 0·001, respectively) for the tree at Kawerau (see Table 2).

Variation in δ18O

Seasonal patterns in δ18O of cellulose were not as consistent as for δ13C. Generally a summer maximum was found, but enrichment varied considerably over the season. The average δ18Oc for each site followed 13C trends, with Balmoral having the most enriched δ18Oc, at 30·6‰, then Matangi at 30·1‰ and Kawerau at 29·8‰. However, ranking for extent of seasonal variation in δ18Oc was reversed compared to δ13Cc. The tree from Kawerau showed the greatest variation in δ18Oc over the two seasons, from 27·5 to 33·0‰, a range of 5·5‰. Balmoral was slightly lower at 5·3‰ and Matangi the lowest at 4·4‰. The broad seasonal patterns of δ18Oc found for the tree from Matangi compared very well to previously published patterns from a Pinus radiata tree growing at a site quite close to the Matangi site (Wilson & Grinsted 1978).

The tree from Balmoral differed from the other two sites in having two peaks in enrichment of δ18Oc in each season; one in spring and the other in autumn (Fig. 3). The midsummer depression of enrichment was very marked in the first season (Fig. 3, marked ‘1’), with δ18Oc of about 29‰ during November and December following a sharp peak up to 32·9‰ in September Table 2 shows that, unlike δ13Cc, δ18Oc was not correlated with either VPD or SWL for the samples from Balmoral.

A sharp midsummer peak in enrichment of δ18Oc was found for the Matangi tree during the first season, the peak in enrichment coinciding with the peak in enrichment in δ13Cc (Fig. 4,  marked  ‘1’).  The  maximum  enrichment  for the first season was 32·6‰, followed by a winter minimum of  28·6‰.  A  summer  increase  in  enrichment  was  also found the next season, although δ18Oc fluctuated quite a bit and reached a maximum enrichment of just 31·6‰. δ18Oc was  found  to  be  significantly  positively  related  to  both VPD and SWD (P < 0·001 and P < 0·01, respectively, see Table 2).

The δ18O of cellulose from the tree at Kawerau during the first season had a similar pattern to that of the second season at Matangi, that is an increase during spring then fluctuating over summer and decreasing to a low during autumn (Fig. 5). Enrichment of 18O during spring and early summer of the second season was fairly constant at about 28·8‰, then increased in enrichment rapidly to a sharp peak of 33·0‰ in January, 1993 (Fig. 5, marked with an arrow). The δ18Oc was significantly (P < 0·0001) positively related to SWD for samples from Kawerau, but showed no significant relationship with VPD (see Table 2).

The δ18Oc generally fluctuated more than δ13Cc during an annual cycle. δ18Oc and δ13Cc follow similar patterns for some seasons, but in other seasons the two differ markedly. For example, patterns of enrichment at Balmoral were very similar for δ13Cc and δ18Oc for the first season, with two peaks, but in the second season δ18Oc also showed two peaks, whereas δ13Cc had only one. At Matangi δ13Cc and δ18Oc had very similar patterns during both seasons. At Kawerau, the sharp peak in enrichment during the second season was much greater for δ18Oc than for δ13Cc, although the timing was identical.

Correlations between δ13Cc and δ18Oc

The δ13Cc and δ18Oc were positively correlated at all three sites, although the slope varied between sites (Fig. 6). Kawerau had the steepest slope, with an increase of 2·17‰ in δ18Oc per 1‰ increase in δ13C, and a correlation coefficient of r = 0·63. The tree at Balmoral had an intermediate slope at 1·57, and some scatter of points around the fitted line: r = 0·52. The shallowest slope between δ13Cc and δ18Oc was found for the tree at Matangi, which had a slope of 0·95‰δ18Oc per 1‰δ13Cc, but the highest correlation coefficient: r = 0·77.

Figure 6.

Relationships between δ13C and δ18O of cellulose for trees at (a) Balmoral; (b) Matangi; and (c) Kawerau. For (a) δ18Oc = 69·1 + 1·57 δ13Cc, r = 0·52. For (b) δ18Oc = 54·6 + 0·95 δ13Cc, r = 0·77. For (c) δ18Oc = 88·5 + 2·17 δ13Cc, r = 0·63.

To compare these data to those presented in Saurer et al. (1997), average δ13Cc and δ18Oc for each site are plotted. Figure 7 shows the close correlation between the two, with a line of best fit through

Figure 7.

The relationship between site averages of δ13C and δ18O of cellulose. δ18Oc = 38·0 + 0·30 δ13Cc, r = 0·998, P = 0·034.

δ18Oc  =  38·1  +  0·30δ13Cc, r  =  0·998.(12)

The oxygen isotope composition of cellulose was found to be negatively related to the modelled annual value of rainfall δ18O, with a decrease in cellulose of 0·22‰ for a 1‰ increase in soil water, as shown in Fig. 8. A positive relationship between δ18Oc and source water δ18O is generally found (e.g. Roden & Ehleringer 1999a), and the negative relationship found here highlights the differences in the leaf evaporative environment, and possibly also the soil evaporative environment, between these three sites.

Figure 8.

The relationship between average modelled δ18O of rainfall and measured δ18O of cellulose for each site. δ18Oc = 28·8–0·22δ18OR, r = −0·99, P = 0·019.

The slope of the relationship between δ13Cc and δ18Oc tended  to  increase  with  increasing  annual  average  VPD, as shown in Fig. 9, although the relationship was not ­significant.

Figure 9.

The relationship between average annual vapour pressure deficit (VPD) and the dependence of δ18Oc on δ13Cc (δ18Oc:δ13Cc slope) for each site.


The δ13Cc tended to increase to a peak during the late-summer period for all sites. The exception was the first season at Balmoral, which showed a midsummer decrease in δ13Cc followed by a late-autumn peak. As discussed by Walcroft et al. (1997) such seasonal patterns in δ13Cc represent a record of the interaction between seasonally variable micrometeorological factors, soil water status, and the plant response to its evaporative environment. Differences in atmospheric and soil water availability between sites were also reflected in the average δ13Cc for each site, with the highest average δ13Cc value at the driest site (as found for wood δ13C by Walcroft et al.)

The range in cellulose δ13C values was the highest (5·9‰) at Matangi, the site with an intermediate annual rainfall. This is a little surprising as Walcroft et al. (1997) found the greatest range in wood δ13C at Balmoral, the driest site. However, very high δ13Cc values were found over a brief period of high (for Matangi) atmospheric and soil water stress during the summer of the first season (see ‘1’ in Fig. 4f). These five very high δ13Cc values extend the range by about 2‰ for the first (droughted) season. A range of 5·9‰ in the first season compares to just 2·6‰ in the second. The combination of high atmospheric and soil water stress in the first season is unusual for Matangi, so that for a longer-term sampling period the range in δ13Cc would probably sit between the drier Balmoral site and the wetter Kawerau site. However, the driest site did have a greater range in cellulose δ13C than the wettest site, in agreement with ranges in δ13C of wood presented by Walcroft et al. (1997).

These data show, for the first time, that δ18Oc also displays coherent seasonal patterns of enrichment. δ18Oc generally showed an increase in enrichment during the spring (days 50–150 and 450–550 in Figs 3–5) and a depletion during autumn (days 250–350 and 600–700 in Figs 3–5). These trends are probably strongly driven by seasonal variation in source water δ18O. Specific events, such as unseasonally high rainfall in the first summer at Balmoral and soil water deficit during the first summer at Matangi, are clearly recorded in δ18O of cellulose. δ18Oc also seemed to record fluctuations in soil water deficit (probably due to the effects of SWD on control of water loss), with significant positive correlations between the two at both the Matangi and Kawerau sites.

The positive relationship between VPD and δ18Oc predicted by theory (see Fig. 1d) was found at only one site of the three studied. However, this does not necessarily mean that the theory is incorrect, but probably indicates other effects on δ18Oc, such as variation in source water δ18O.

The periods of time at each site when δ13Cc and δ18Oc do not follow the same pattern of enrichment are of particular interest, and suggest that additional information about plant growth conditions may be obtained if the two are measured simultaneously. The seasonal changes in temperature and VPD were similar for both seasons at Balmoral, suggesting that the seasons may have had similar patterns of ea/ei, and so of δ18Oc. However, a summer soil water deficit experienced in the second season alone resulted in a decline in ci/ca (Walcroft et al. 1997) and a broad mid-summer peak in δ13Cc which was not evident in the first season. During the second season at Kawerau a very sharp increase in enrichment of δ18Oc was found, with a smaller, coinciding peak in δ13Cc. The difference in the height of the peaks for δ18Oc and δ13Cc may be due to the combination of high VPD and low soil water deficit during this period (days 560–620, Fig. 5). The high temperatures and VPD would have resulted in large increases in leaf water enrichment, and so δ18Oc. However, water was not limiting so that gs did not need to be greatly reduced to control water loss, meaning that ci remained relatively high and δ13Cc did not increase sharply. This combination of changes in δ18Oc and δ13Cc can be compared to the midsummer drought in the first season at Matangi, when a combination of soil water deficits and high temperatures seemed to result in sharp peaks in both δ18Oc and δ13Cc.

The significant, positive correlations between δ13Cc and δ18Oc at each site support the hypotheses presented in the introduction. Such positive relationships have been found for a number of other experimental systems, such as leaf cellulose from tropical forest trees (Sternberg, Mulkey & Wright 1989), tree ring cellulose from three species across a moisture gradient (Saurer et al. 1997), and whole leaf tissue from cotton (Barbour & Farquhar 2000) and wheat (Barbour et al. 2000a). The slope of the δ13C : δ18O relationship varies between the different experimental systems, with the steepest slope (2·9‰ increase in δ18Ol per 1‰ increase in δ13Cl) found for whole flag leaves of irrigated wheat (Barbour et al. 2000a) and the shallowest slope (0·32‰ increase in δ18Oc per 1‰ increase in δ13Cc) for the tropical forest tree Tetragastris panamensis (Sternberg et al. 1989). Variation in slope between sites was also found in this experiment, with the steepest slope at the warmest site.

The steep slope found at the warm Kawerau site, when compared to the relationship for the tree at the Matangi site (2·17 and 0·95‰ increase in δ18Oc per 1‰ increase in δ13Cc, respectively), supports the theory outlined in the introduction, i.e. that a greater change in δ18Oc per unit change in δ13Cc will be found when VPD is higher (see Fig. 2).

Because the effects of seasonal variation in δ18Os on δ18Oc are not included in the model, the actual values of the slope of the δ18Oc : δ13Cc relationship found for field-grown trees could not be directly compared with modelled values. To compare measured and modelled slopes, both must be presented as the dependence of changes in enrichment in 18O of cellulose above source water (Δ18Oc) on changes in δ13Cc, which is only possible if soil water samples are taken for δ18O analysis throughout the season.

Site averages for δ13Cc and δ18Oc were also found to be positively related. The slope of the relationship (0·30‰ change in δ18Oc per 1‰ change in δ13Cc) matches exactly, but probably fortuitously, the slope found in Pinus sylvestris by Saurer et al. (1997). An interesting finding is that a negative relationship (P = 0·02) exists between site average δ18Oc and modelled annual weighted mean δ18O of soil water (Fig. 8). This is the reverse of the predicted relationship, and presumably illustrates the influence of climate-mediated leaf processes on δ18O of stem cellulose. The negative relationship suggests that the site with the most depleted rainfall, Balmoral, also had the greatest leaf water enrichment (and possibly also the greatest surface soil water enrichment). Such an interpretation seems reasonable given that Balmoral had the lowest annual average rainfall and the highest midsummer VPD.

The interacting nature of the driving environmental variables seems to result in poor correlations between isotope ratios and single environmental variables. For example, δ13Cc was significantly related to soil water deficit at only two of the three sites, and δ18Oc was significantly related to VPD at only one site. Walcroft et al. (1997) and Berninger et al. (2000) have successfully shown that a process-based modelling approach can integrate temporal variation in environmental variables and corresponding plant response, so that seasonal (Walcroft et al. 1997) and long-term annual (Berninger et al. 2000; Arneth et al. 2002) variation in tree ring δ13C may be accurately modelled. The appropriate temporal scale at which to apply the models described in this paper will depend on the scale at which environmental data (for model inputs) and isotope data (for model validation) are collected. In a future paper we will develop a process-based integrative model to predict the seasonal variation in δ13Cc apparent in these samples, with a temporal resolution of days to weeks.


Both δ13Cc and δ18Oc of tree ring cellulose tended to increase to a peak in midsummer. Specific events, such as droughts, high temperatures and VPD, and higher than average rainfall were clearly recorded in the seasonal ­pattern of cellulose δ13C and δ18O. Positive correlations between δ13Cc and δ18Oc were found for all three sites. As predicted by theory, the slope of the relationships between δ18Oc and δ13Cc increased with increasing average annual VPD. The observation of a negative relationship between site averages for δ18Oc and modelled rainfall δ18O demonstrates the importance of consideration of physiological effects on δ18Oc if variation in δ18Oc is to be interpreted in terms of climate-driven variation in δ18Os.


We acknowledge help with stable isotope analysis from Dr B. K. Henry and Ms. S. Wood, helpful comments by Dr T. Dawson, and support from Micromass UK Ltd.

Received 20 December 2001;received inrevised form 29 May 2002;accepted for publication 31 May 2002

Appendix a

The theory and models presented in the introduction were used to predict changes in δ18Oc and δ13Cc in response to changes in relative humidity. Sheriff & Mattay (1995) have shown that gs (mmol m−2 s−1, on a projected leaf area basis) in Pinus radiata may be expressed as a function of foliar nitrogen concentration (N, mmol m−2), leaf temperature (Tl, °C) and leaf-to-air vapour pressure difference (Dla, mbar) by:

gs  =  (N  −  α)(β  +  (σ  +  1/Dla)(τ  +  δ(Tl  −  ɛ)2)),((A1))

where α, β, σ, τ, δ, and ɛ are fitted parameters. To predict gs from Dla, fitted values for these parameters were used (α = 22·2, β = 2·777, σ = 0·317, τ = 5·374, δ = 0·00784 and ɛ = 24·02; Sheriff & Mattay 1995) and the mean value of foliar nitrogen concentration found by Sheriff & Mattay used (N = 103 mmol m−2, again on a projected leaf area basis). Leaf temperature was assumed to be equal to air temperature (constant at 20 °C) as suggested by Walcroft et al. (1997). This assumption is discussed in more detail in Appendix B. Stomatal conductance values used by Sheriff & Mattay (1995) to fit Eqn A1 were collected in a gas exchange cuvette on a projected area basis. Predicted gs values were converted to a total leaf area basis, compatible with the photosynthetic capacity value used (30 µmol m−2 s−1; Walcroft et al. 1997), by dividing by π (Grace 1987).

Following von Caemmerer & Farquhar (1981), and ­incorporating dark respiration into the CO2 compensation point term (Γ), Rubisco-limited photosynthesis (A) is given by:


where Vcmax is the photosynthetic capacity of the leaf and ci is the intercellular CO2 concentration. In Eqn A2,

K′  =  Kc(1  +  o/Ko),((A3))

where Kc and Ko are the Michaelis constants for CO2 and O2, and o is the intercellular oxygen concentration. A may also be given by:

A  =  gsc(ca  −  ci),((A4))

where gsc is the stomatal conductance to CO2 (gsc = gs/1·6), and ca is the atmospheric CO2 concentration. Rearranging Eqn A4 in terms of ci gives:

ci  =  ca  −  (A/gsc),((A5))

and substituting Eqn A5 into Eqn A2 gives:


It can be shown that:


where M = gsc(ca + K′) and gsc is in units of mol m−2 s−1. Eqn A7 is used to predict A from gs given by Eqn A1. Vcmax is assumed to have a default value of 30 µmol m−2 s−1 at 20 °C, Γ is assumed to be 70 µmol mol−1 and K′ is 550 (Walcroft et al. 1997). The value of ci is calculated from predicted gsc and A using Eqn A5, and δ13Cc from Eqn 3, assuming a = 4·4‰, b = 27‰, δ13Ca = −7·8‰ and ɛc-p = 2‰.

The enrichment of water at the sites of evaporation within the leaf above source water (Δ18Oe) is given by (Farquhar & Lloyd 1993):

Δ18Oe  =  ɛ*  +  ɛk  +  (Δ18Ov  −  ɛk)(ea/ei),((A8))

where ɛ* is the proportional depression of water vapour by H218O, ɛk is the kinetic fractionation, Δ18Ov is the enrichment of atmospheric water vapour above source water and ea and ei are atmospheric and intercellular vapour pressures. As leaves are assumed to be at the same temperature as air, ei is given by the saturated vapour pressure at air temperature (23·48 mbar at 20 °C), and ea given by the VPD chosen (default of 0·94 kPa). Bulk leaf water enrichment is calculated using Eqn 6, assuming L is 8 mm (Barbour et al. 2000a), and the evaporation rate (E, mol m−2 s−1) is given by [(Dla/P) × gs], where P is total pressure in mbar.

Cellulose 18O enrichment above source water is given by Eqn 8, where pex = 0·5, px= 1 and ɛwc = 27‰. As 18O values in this paper are presented relative to the VSMOW standard, Δ18Oc values are converted (to a close approximation) to δ18Oc values by:

δ18Oc ≈ Δ18Oc  +  δ18Os,((A9))

where δ18Os is the source water, and assumed to be −8·0‰.

Appendix b

An important assumption in the model of δ18Oc and δ13Cc for Pinus radiata presented in Appendix A is that the leaf is strongly coupled to the environment, making leaf temperature the same as air temperature. This is important because it means that changes in gs do not alter the evaporative cooling of the leaf, and ei and ɛ* scale directly to air temperature. If increased stomatal conductance enhanced evaporative cooling and the leaf became cooler than the air (i.e. the leaf is uncoupled from the atmosphere), then ei would decrease and ɛ* would increase, resulting in a lower Δ18Oe (Eqn A8). This reduction in Δ18Oe is reinforced by the Péclet effect (Eqn 6). The effect of leaf evaporative cooling on δ18Oc is to increase the response of δ18Oc to changes in gs.

To demonstrate this effect a tree species with larger leaves, peach (Prunus persica), was modelled in the same way as Pinus radiata. The response of gs to changes in Dla differs between the species, so data were extracted from Fig. 4b of Turner, Schulze & Gollan (1984), and the best fit (r2 = 0·92) of gs (in mmol m−2 s−1) on Dla (in mbar) obtained with:

gs  =  269·8  −  4·4Dla((B1))

Equation B1 was used in place of Eqn A1 in the model, and the default value of Vcmax changed to 60 µmol m−2 s−1 at 20 °C (estimated from Prunus persica at 30 °C in Le Roux et al. 2001; and other broad-leaved species in Dreyer et al. 2001).

The difference between leaf and air temperatures (ΔT) was modelled as described in Barbour et al. (2000b) following DGG dePury & GD Farquhar (unpublished):


where r*bH is the combined resistance to sensible and radiative  heat  transfer  in  parallel  (assumed  to  be  0·48 m2 s mol−1), rs and rb are the stomatal and boundary layer ­resistances to water vapour (1/gs and assumed to be 0·473 m2 s mol−1, respectively), Q0 is the isothermal net radiation (assumed to be 173·9 W m−2), L is the molar heat of vaporization (44 012 J mol−1), Cp is the molar specific heat constant of air (29·2 J mol−1 K−1), and ɛ is the change of latent heat content of saturated air with a change in sensible heat content (2·192 at 20 °C).

Including a leaf temperature submodel results in ei differing from the saturation vapour pressure of the air outside the leaf, unlike the model for Pinus radiata, and means that both ɛk and ɛ* vary with VPD at constant air temperature. The greater sensitivity of δ18Oc to changing gs modelled for Prunus persica compared with Pinus radiata may be seen by contrasting Fig. B1e with Fig. 1e. The greater sensitivity of δ18Oc to gs also means that the slope of the δ18Oc : δ13Cc relationship is steeper. Figure B2 shows that when gs alone varies, the slope of the δ18Oc : δ13Cc relationship at 0·94 kPa VPD is 0·73‰ ‰−1, whereas the modelled slope for Pinus radiata at 0·94 kPa VPD is just 0·05‰ ‰−1 (see Fig. 2). The modelled differences in sensitivity of δ18Oc to changing gs between strongly coupled trees (Pinus radiata) and those uncoupled from the atmosphere (Prunus persica) are also interesting given the differences in estimated Péclet numbers observed by Wang et al. (1998) between conifers and other growth forms. This difference is most likely due to lower transpiration rates per unit leaf area for conifers, but may also be due to inherently different effective lengths between conifers and broad-leaved plants.

Figure B1.

The modelled relationship between δ13C and δ18O of cellulose for Prunus persica when: (a) and (d) vapour pressure deficit varies; (b) and (e) stomatal conductance varies; (c) and (f) photosynthetic capacity varies. The δ13Cc and δ18Oc models used are described in Appendix B. Default values used were: VPD = 0·94 kPa, gs = 0·230 mol m−2 s−1, Vcmax = 60 µmol m−2 s−1. Source water δ18O was assumed to be constant at −8·0‰.