Evaluation of models of leaf water 18O enrichment using measurements of spatial patterns of vein xylem water, leaf water and dry matter in maize leaves

Authors

  • K. S. GAN,

    1. Environmental Biology Group, Research School of Biological Sciences, Australian National University, Australia
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  • S. C. WONG,

    1. Environmental Biology Group, Research School of Biological Sciences, Australian National University, Australia
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  • J. W. H. YONG,

    1. Environmental Biology Group, Research School of Biological Sciences, Australian National University, Australia
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    • *

      Present address: Natural Sciences Academic Group, National Institute of Education, Nanyang Technological University, Singapore.

  • G. D. FARQUHAR

    Corresponding author
    1. Environmental Biology Group, Research School of Biological Sciences, Australian National University, Australia
      Graham D. Farquhar. Fax: +61 2 6125 4919; E-mail: farquhar@rsbs.anu.edu.au
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Graham D. Farquhar. Fax: +61 2 6125 4919; E-mail: farquhar@rsbs.anu.edu.au

ABSTRACT

The effectiveness of several leaf water models (‘string-of-lakes’, ‘desert river’ and the Farquhar–Gan model) are evaluated in predicting the enrichment of leaf water along a maize leaf at different humidities. Progressive enrichment of both vein xylem water and leaf water was observed along the blade. At the tip, the maximum observed enrichment for the vein water was 17.6‰ at 50% relative humidity (RH) whereas that for the leaf water was 50‰ at 34% RH and 19‰ at 75% RH. The observed leaf water maximum was a fraction (0.5–0.6) of the theoretically possible maximum. The ‘string-of-lakes’ and ‘desert river’ models predict well the variation of leaf water enrichment pattern with humidity but overestimate the average enrichment of bulk leaf water. However, the Farquhar–Gan model gives good prediction for these two aspects of leaf water enrichment. Using the anatomical dimensions of vein xylem overestimates the effective longitudinal Péclet number (Pl). Possible explanations for this discrepancy between the effective and the xylem-based estimate of Pl are discussed. The need to characterize the heterogeneity of transpiration rate over the leaf surface in studies of leaf water enrichment is emphasized. The possibility that past atmospheric humidity can be predicted from the slope of the Δ18O spatial variation of leaf macrofossils found in middens is proposed.

INTRODUCTION

The isotopic enrichment of leaf water during transpiration is most commonly associated with the Craig–Gordon model (Craig & Gordon 1965), which can be modified, to a reasonable approximation, to describe the enrichment of leaf water at the sites of evaporation (Dongmann et al. 1974; Farquhar et al. 1989):

image(1)

where ΔC denotes the Craig–Gordon estimate of the isotopic enrichment of leaf water above source water as described by this equation; Δv the enrichment of atmospheric water vapour above source water; e+ and ek the equilibrium and kinetic fractionation factors, respectively; ea and ei the water vapour pressures in the atmosphere and intercellular spaces, respectively. A full list of symbols and their definitions is given in the Appendix. As more measurements of leaf water were made, experimenters noted that the Craig–Gordon model tends to overestimate the isotopic enrichment of leaf water, Δlw (Allison, Gat & Leaney 1985; Walker et al. 1989; Yakir, DeNiro & Gat 1990; Flanagan, Bain & Ehleringer 1991; Flanagan, Comstock & Ehleringer 1991; Flanagan et al. 1994; Wang, Yakir & Avishai 1998; Roden & Ehleringer 1999) and is not able to account for the spatial variation of Δlw (Luo & Sternberg 1992; Bariac et al. 1994; Wang & Yakir 1995; Helliker & Ehleringer 2000, 2002; Gan et al. 2002). To explain these observations, more leaf water models have been proposed in conjunction with the Craig–Gordon model. The two-pool model (Leaney et al. 1985) describes leaf water as a composite of enriched leaf tissue water and non-enriched vascular water. The Péclet model (Farquhar & Lloyd 1993) accounts for the ‘micro’ variation of leaf water enrichment between the vein and the sites of evaporation by considering the relative effects of advection and diffusion. The ‘string-of-lakes’ model (Gat & Bowser 1991; Yakir 1992; Helliker & Ehleringer 2000, 2002) predicts a ‘macro’ spatial variation across the entire leaf surface based on the progressive enrichment of leaf water along the path of evaporation. Comprehensive reviews of the various leaf water models can be found (Yakir 1992, 1998; Gan et al. 2002).

From a study of the 18O spatial patterns of vein xylem water, leaf water and dry matter in cotton leaves grown at different humidities, Gan et al. (2002) demonstrated that leaf water in dicotyledoneous plants has different isotopic enrichment patterns at different humidities, resembling the behaviour of a string of interconnected evaporating lakes. The analogy of the leaf water pathway to the movement of water through a sequence of lakes in series was previously noted in monocotyledoneous plants (Yakir 1992; Helliker & Ehleringer 2000) but deemed to be less appropriate in dicotyledoneous leaves (Helliker & Ehleringer 2000). To account for the observations that vein xylem water is partly enriched in comparison with source water, and bulk leaf water less enriched than the Craig–Gordon prediction, ΔC, Gan et al. (2002) highlighted the need to include Péclet effects (advection from the vein opposing diffusion from the sites of evaporation) in the ‘string-of-lakes’ model for its application to leaves. Gan et al. (2002) envisaged the competing effects of the transpiration flux and the back-diffusion of enriched water to occur in two dimensions, longitudinally along the leaf length as well as radially in the plane of the leaf lamina, from the vein network to the leaf evaporative sites. Gan et al. (2002) also identified the presence of capacitance in the ground tissues of vein ribs to be one reason for the lower enrichment of bulk leaf water.

On the basis of these findings (Gan et al. 2002), Farquhar & Gan (2003) developed a leaf water model featuring aspects of progressive enrichment, two-dimensional Péclet effects and ground tissue capacitance. As a first step in the leaf water modelling, Farquhar & Gan (2003) showed how the ‘string-of-lakes’ model could be modified to describe a continuous treatment of evaporative sites in leaves, as opposed to the discrete number of evaporating elements in the Gat–Bowser formulation where

image(2)

where δv and δn are the isotopic composition of atmospheric water vapour and of water entering the nth evaporating element, respectively, F+ and E represent the influx and evaporative efflux of the nth element, h is the relative humidity and e = e* + (1 − h)ek[note that e* = e+/(1 + e+)]. Continual loss of water by evaporation in leaves resembles a desert river system, first introduced by Fontes & Gonfiantini (1967). According to Farquhar & Gan (2003), the enrichment of leaf water, Δlw, at a relative distance l/lm from the leaf base of a leaf lm long, can be written with respect to the maximum possible enrichment, ΔM, as follows:

image(3)

where

image(4)

and

image(5)

For the same order of approximation as Eqn 1, h′ ≈ h, where h is the relative humidity at the leaf temperature (equal to ea/ei). For a more realistic modelling of the enrichment of leaf water, Farquhar & Gan (2003) also took into account the presence of Péclet effects along the longitudinal and radial dimensions of a leaf blade and the significant pool of ground tissue water in the vein ribs. Considering first the modelled radial Péclet effect, an isotopic gradient, on the plane of the leaf lamina, develops from the major vein xylem, through the leaf mesophyll and onwards to the evaporative sites. The enrichment of the vein xylem water, Δx, is lower than the radial average enrichment of water in the mesophyll of the lamina, Δl, which in turn is lower than the enrichment at the sites of evaporation, Δe. The enrichment of these water compartments (Δx, Δl and Δe) varies with the longitudinal length, l, along the main axis of the leaf, due to longitudinal Péclet effects sustaining the progressive enrichment along a line of evaporating cells. Note that unlike the conventional treatment of leaves, which takes Δe to be equal to ΔC, the present model allows Δe to vary spatially, and so to differ from ΔC. For ease of comparison with experimental data, the modelled Δx, Δl and Δe are normalized against the maximum possible enrichment, ΔM, and their variations are expressed with respect to l/lm as follows (Farquhar & Gan 2003):

image(6)
image(7)
image(8)

where inline image; Pr, P and Pl are the total radial Péclet

number, lamina radial Péclet number and longitudinal Péclet number, respectively. The expression 1F1[a, b; z] is the Kummer function describing a confluent hypergeometric series and can be computed using mathematical software packages, for example MATHEMATICA, MAPLE and DERIVE 5 (Farquhar & Gan 2003). In the work described in this paper, MATHEMATICA (Version 4.1, Wolfram Research, Champaign, IL, USA) was used for the computation of the Kummer function.

As illustrated by Gan et al. (2002), the enrichment of leaf water in cotton leaves does not occur in an uni-dimensional direction from the leaf base to the tip. Distinct regions of higher or lower enrichment have been identified. Such complex enrichment patterns are attributed to the reticulate venation of cotton leaves. This venation complexity makes the measurement of vein water path-length (l/lm) near impossible, and deters us from fitting the observed values of leaf water (Δlw) and vein xylem water (Δx) enrichment to Eqn 6 for quantitative assessment of the Farquhar–Gan model. The maize leaf, on the other hand, has long and minimally branched parallel veins typical of a monocotyledoneous plant. This enables the total water pathway along the longitudinal direction to be represented by the full length of the leaf blade. The maize leaves could thus form a good system for studying water distribution and isotopic fluxes. Nevertheless, the Farquhar–Gan model is a simplification of what happens in maize leaves where there are many longitudinal xylem elements of different length, lm, in a single leaf.

In this paper, we present experimental results on the spatial variation of leaf water enrichment along a maize leaf, at different humidities, for comparison with the predicted values of the leaf water models described above. Concurrently, the enrichment of vein xylem water was also studied. Next, Péclet numbers along the longitudinal and radial dimensions were estimated from anatomical dimensions, vein xylem water and bulk leaf water isotope measurements. Farquhar & Gan 2003) have indicated that the radial Péclet number (Pr) is likely to be of order one whereas the longitudinal Péclet number (Pl) estimated from the anatomical dimensions of vein xylem could be of order 107. They also highlighted that with the consideration of advection and diffusion in the longitudinal dimension in the lamina (a feature yet to be incorporated in their model), the effective Pl value should be smaller and somewhere between this xylem-based value and Pr. This article aims to assess the extent of agreement between the anatomical estimate of Pl in the xylem, and the effective Pl as observed from the experimental data of leaf water enrichment of maize leaf segments.

MATERIALS AND METHODS

Plants of Zea mays (Yates, sweet corn, cv. premium) were grown under full sunlight in two glasshouses at the same temperature (30 ± 1 °C day, 22 ± 1 °C night) but with different relative humidities (20–40% and 65–80%). Accurate measurements of relative humidity were also made at the time of sampling in individual experiments. The plants were fertilized with a slow-release fertilizer (Osmote Plus Scotts; Sierra Horticultural Products, The Netherlands) and watered with tap water (δs = −7.3 ± 0.1‰) twice daily. Atmospheric water vapour was collected using a dry ice-ethanol cold trap, giving δv = −11.6 ± 0.3 (SD)‰. All samplings and measurements were carried out on fully expanded leaves of plants that were 20 to 30 d old in the glasshouses on cloud-free days during the time period of 1100–1500 h when gas exchange was observed to be at steady state. Measurements of leaf gas exchange were taken at mid-length of the leaf blade using a portable gas exchange system (model LI-6400; Licor Inc., Lincoln, NE, USA) at a photosynthetic photon flux density (PPFD) of 1200 µmol m−2 s−1 from a LED light source. Boundary layer conductance in the glasshouses was measured to be 0.52 ± 0.04 mol m−2 s−1 (Gan et al. 2002). With the kinetic fractionation factor having a value of 28.5‰ for diffusion through stagnant air (Merlivat 1978) and 18.9‰ in the laminar flow boundary layer, the overall kinetic fractionation factor was calculated to be 25.2‰, after applying the mean values of leaf stomatal and boundary layer conductances to the equation provided by Farquhar et al. (1989).

Vein xylem water sampling

To map the spatial variation of vein water enrichment, xylem water was collected from the midrib and lateral veins (Fig. 1) at various distances along the leaf. The procedures of root pressurization using a root pressure chamber (Yong et al. 2000), vein incision and the collection of xylem sap were described in Gan et al. (2002). Spatial mapping of the enrichment of vein xylem water was carried out on a single leaf at a relative humidity of 50%. In another experiment studying humidity effects on the isotopic composition of vein xylem water, a step change of humidity was carried out on two maize plants (one undergoing a step change from low to high humidity, the other from high to low humidity). For two leaves of each plant, xylem sap was collected from a series of incisions on the midrib and lateral veins one-third of the leaf back from the tip. One hour after the step change of humidity, xylem water was again collected from the same vein incisions.

Figure 1.

Spatial distribution of vein xylem water enrichment, Δx (‰), of a maize leaf (leaf position 3 from the base, 50 cm long, 3.5 cm at the widest point) at 50% relative humidity (air temperature, 30 °C; VPD of air, 2.12 kPa; ea/ei = 0.399; h′ = 0.378 according to Eqn 5). The marking × denotes vein incision locations and the downward sequence of a cluster of numbers represents the Δx of parallel veins in sequence from the midrib to the edge. The symbols * and ♯ indicate Δx belonging to the same continuous parallel vein, sampled from distal to proximal. Top inset illustrates the organizational structure of veins in the maize leaf. Bottom inset illustrates the variations of Δx of the midrib (◆), and the marginal lateral vein (□) with relative distance from the leaf base, where 1.0 on the abscissa refers to the leaf tip. The dotted line curve is a re-scale of the line representing the marginal lateral vein by setting 1.0 on the abscissa to be the full length of the marginal vein rather than the leaf length (as the marginal vein terminates at 0.7 of full leaf length).

Leaf water and organic matter sampling

For bulk leaf water analysis, four whole leaves of positions 3 and 4 (measured from the base of the plant) and the corresponding leaf sheaths were sampled for each humidity treatment. Two of the leaves had the midrib vein removed before freezing and storage in screw-cap glass culture tubes. The percentage of leaf water associated with the midrib was determined by gravimetric analysis as described by Gan et al. (2002). Leaf water was extracted by vacuum distillation and the remaining dried leaf blades were ground for isotopic analysis of leaf organic matter.

To determine the spatial variation of leaf water enrichment, four other leaf blades (positions 3 and 4) at each humidity were divided along the length into 5 cm segments, with the midrib vein removed in two of the replicates. The leaf segments and leaf sheath samples were immediately frozen in screw-cap culture tubes for leaf water extraction by vacuum distillation. Thereafter, the residual dried leaf segments were ground for isotopic analysis of leaf organic matter.

Oxygen isotope analysis

Oxygen isotopic analyses of water and dry leaf materials were all performed using the continuous-flow pyrolysis technique described by Farquhar, Henry & Styles (1997) with slight modifications (Gan et al. 2002). The isotopic internal standard for water samples was ANU-OW (δ18O = 0.50‰, Research School of Earth Sciences, Australian National University, Canberra, Australia) while standards of beet sucrose (δ18O = 30.81‰) containing 1, 2 or 3% nitrogen (from adding 2-aminopyrimidine) were used for correcting the isotopic composition of dry leaf samples according to their nitrogen contents. The analytical precision based on the measurements of these standards ranged from 0.2 to 0.5‰. Preparation of water and solid samples for pyrolysis was similar to that discussed by Gan et al. (2002).

Anatomical measurements

Transverse sections of fresh leaf material were taken at various distances along the blade and mounted ‘upright’ on metal stubs using a mixture of an embedding medium (TissueTek O.C.T. Compound 4583; Miles Scientific, Naperville, IL, USA) and colloidal graphite. They were then frozen in liquid nitrogen and fractured by hand with a single edged razor blade. Scanning electron microscope (Hitachi S-2250N; Hitachi High-Technologies Corporation, Tokyo, Japan) images were taken as in Gan et al. (2002) and measurements made of the xylem vessel diameters and interveinal distances.

RESULTS

Δ18O patterns of vein xylem water

Along the leaf blade, a progressive enrichment of xylem water was observed in all parallel veins (Fig. 1). Enrichment of vein xylem water over source water (Δx) was highest near the leaf tip with the midrib vein achieving Δx of 17.6‰ at a relative humidity of 50%. At any particular distance along the leaf blade, the enrichment of xylem water in the parallel lateral veins increased on going from the midrib towards the leaf margin. This midrib-to-edge Δx difference also increased along the leaf length, reaching a maximum (6‰) at around mid-way along the leaf (Fig. 1, bottom inset).

The isotopic composition of vein xylem water responded to the step changes of ambient humidity (Table 1). Irrespective of the direction of humidity step change, xylem water was always more enriched at low humidity, with a difference (between humidities) as high as 25‰ for the vein closest to the leaf margin, which is approaching its terminus. When the observed enrichment of xylem water was normalized against the Craig–Gordon prediction, ΔC, the mean of ΔxC for all the vein incisions was also higher for low humidity leaves (P < 0.02). Values of ΔxC one-third length away from leaf tip ranged from 0.16 in the midrib vein to 1.22 in the marginal vein, with a general trend of increasing ΔxC from the midrib vein to the leaf margin. The effect of humidity change on gas exchange parameters is summarized in Table 1. Increasing the ambient humidity had little impact on the stomatal conductance despite a significant decrease in leaf transpiration rate.

Table 1.  Δx (‰) and ΔxC of vein xylem water from maize leaves before and after a step change of humidity (h) for two different leaves of the same plant (first line for leaf position 3, second line for leaf position 4)
IncisionΔx (‰)ΔxC
Low → High humidityHigh → Low humidityLow → High humidityHigh → Low humidity
Low h
h′ = 0.200
High h
h′ = 0.496
DifferenceHigh h
h′ = 0.520
Low h
h′ = 0.259
DifferenceLow h
h′ = 0.200
High h
h′ = 0.496
DifferenceHigh h
h′ = 0.520
Low h
h′ = 0.259
Difference
  1. Incisions on the midrib (A) and the lateral veins (B–F) were carried out at a distance about one-third from the leaf tip on one side of the midrib. The incisions on the lateral veins are labelled alphabetically starting from the midrib. The vapour pressure deficits of air at low (RH, ∼30%) and high humidity (RH, ∼75%) were on average 3.0 and 1.1 kPa, respectively. The values of h′ (calculated according to Eqn 5) are indicated in the heading. ΔC refers to the enrichment of leaf water above source water (δs = −7.3‰) as calculated according to the Craig–Gordon model. Values of δv and ei were taken from the experiments on leaf water sampling. For low → high humidity experiment, ΔC = 26.7‰ (low humidity) and 17.1‰ (high humidity); high → low humidity experiment, ΔC = 24.9‰ (low humidity) and 16.4‰ (high humidity). Different plants were used for each humidity step change experiment. Gas exchange data were recorded for both plants with the position of the leaf indicated in brackets. Parameters gs, E and A refer to stomatal conductance to water vapour, transpiration rate and assimilation rate, respectively.

A (midrib) 4.3 4.4  0.1 5.3 8.22.90.160.26 0.100.330.33 0.00
 5.1 4.3 −0.8 5.3 8.83.50.190.25 0.060.320.35 0.03
B10.3 6.1 −4.20.390.36−0.03
10.0 7.2 −2.810.214.84.60.370.42 0.050.620.59−0.03
C13.2 5.9 −7.3 7.313.86.50.490.35−0.140.450.55 0.10
12.7 7.1 −5.6 8.515.36.80.480.41−0.070.520.61 0.09
D18.3 6.2−12.110.714.13.40.690.36−0.330.650.56−0.09
17.2 6.9−10.3 9.416.87.40.640.40−0.240.570.67 0.10
E23.2 6.6−16.610.015.55.50.870.38−0.490.610.62 0.01
21.1 7.7−13.410.519.69.10.790.45−0.340.640.79 0.15
F (edge)32.6 7.7−24.910.018.28.21.220.45−0.770.610.73 0.12
23.7 7.8−15.910.920.69.70.890.46−0.430.660.83 0.17
Mean16.0 6.5 −9.5 8.915.16.20.600.38−0.220.540.60 0.06
SE 2.4 0.3  2.2 0.6 1.20.70.090.02 0.080.040.05 0.02
Gas exchange parameters
gs (mol m−2 s−1) 0.33 (L1) 0.39 (L1)  0.28 (L3) 0.30 (L1)       
 0.31 (L2) 0.30 (L2)   0.22 (L2)       
E (mmol m−2 s−1) 9.6 (L1) 5.5 (L1)  4.7 (L3) 8.9 (L1)       
 8.9 (L2) 5.1 (L2)   6.8 (L2)       
A (µmol m−2 s−1)29.2 (L1)23.8 (L1) 31.8 (L3)16.5 (L1)       
32.3 (L2)30.9 (L2)  20.3 (L2)       

Δ18O patterns of leaf water and organic matter

The 18O isotopic enrichment of the bulk leaf water, Δb, extracted from the entire leaf blade was found to be less enriched than ΔC by a factor of 0.28 and 0.40, on average, at low and high humidity, respectively (Fig. 2). With the removal of the midrib, these factors were reduced to 0.18 and 0.25, respectively.

Figure 2.

Discrepancy between the measured Δb of bulk leaf water and the Craig–Gordon prediction, ΔC for whole leaves of maize. The term 1 − ΔbC signifies the non-enriched fraction of the bulk leaf water. Comparison is made between low and high humidity treatments at an air temperature of 30 °C. At low humidity (RH 23%), VPD of air = 3.34 kPa, ea/ei = 0.180 and h′ = 0.152 according to Eqn 5; at high humidity (RH 73%), VPD of air = 1.15 kPa, ea/ei = 0.527 and h′ = 0.511. Unshaded bars refer to the removal of midrib vein. Each bar represent a leaf replicate.

Large progressive enrichment of leaf water, Δlw, was observed along the leaf blade at both humidities (Fig. 3). The base-to-tip Δlw difference in low humidity (39.9‰) was about three times that in high humidity (12.3‰). On approaching the leaf tip (representing the terminus of the water flow path), there was a steeper increase in Δlw at low humidity while the increase in Δlw tended to level off at high humidity. The pattern of leaf water enrichment was also reflected in the leaf dry matter (Δom). However, Δom showed a smaller range of isotopic variation along the length of the leaf. The base-to-tip differences were 17.0 and 5.5‰ at low and high humidities, respectively. In all cases, Δom was higher than Δlw, by 0–29‰ at low humidity and 14–25‰ at high humidity. Of interest is the decreasing trend of Δom −Δlw on approaching the leaf tip, with a steeper gradient for the low humidity treatment.

Figure 3.

Progressive enrichment of leaf water (Δlw, •) and leaf dry matter (Δom, ○) of maize leaf segments (length, 5 cm) along the leaf blade in the direction from the leaf base to the tip. Lengths of leaf blades varied from 55 to 90 cm. At low humidity (RH 34%), VPD of air = 2.70 kPa, ea/ei = 0.268 and h′ = 0.243; at high humidity (RH 75%), VPD of air = 1.07 kPa, ea/ei = 0.580 and h′ = 0.566. Air temperature was 30 °C. For each humidity treatment, there are four replicates, two of which have their midrib vein removed. The Δlw (★) and Δom (⋆) of maize leaf sheath in each leaf replicate are indicated. The Δom − Δlw difference is represented by + and * for the leaf and sheath segments, respectively.

Water extracted from the leaf sheath was more enriched than the source water by 0.5–4‰. The majority of the leaf sheath samples showed an enrichment close to the average of 1.8‰ and the occasional highly enriched samples could be attributed to evaporative enrichment from handling errors. Unlike the leaf blade, isotopic composition of the organic matter of the leaf sheath appears to be less sensitive to growth humidity, with the low humidity Δom marginally higher (by 2.1‰) than its high humidity counterpart. In contrast, Δom of the whole blade (with the midrib intact) for plants grown at low humidity (31.3‰) was 4.7‰ higher than for those grown at high humidity (26.6‰). This difference is smaller than the difference of 10.4‰ obtained from the averaging of the Δom of leaf segments of equal lengths (Fig. 3; low humidity, 41.5‰; high humidity, 31.1‰). The Δom obtained by grinding the entire blade effectively gives the mass-weighted average of Δom, which is expected to be lower than the average Δom (over equal length segments) because leaf segments at the proximal end are wider and heavier in mass but much lighter in their isotopic composition than segments at the distal end.

DISCUSSION

Enrichment of vein xylem water in maize leaves

Recently, Helliker & Ehleringer (2000) analysed the bulk leaf water δ18O of grass leaf sections and observed a progressive enrichment along the leaf blade. They proposed a series of successively enriched pools of xylem water moving towards the leaf tip, taking on the isotopic signature of the back-diffused enriched water from near the stomata. They concluded that leaf water enrichment in grass species is analogous to the Gat–Bowser model of a string of interconnected evaporating lakes. In our study, direct 18O measurements of vein xylem water expressed from the maize leaf confirm experimentally the enrichment of xylem water by the back-diffusion of enriched water from the leaf lamina. This is based on the evidence of progressive enrichment of xylem water Δx towards the leaf tip (Fig. 1), and the sensitivity of Δx to ambient humidity (Table 1). The same observations have been noted for cotton leaves (Gan et al. 2002). The progressive enrichment of xylem water along the leaf length confirms that back-diffusion is actively occurring throughout the length of the vein. However, this back-diffusion of enriched water will not lead to complete isotopic mixing of the lamina mesophyll water and vein xylem water, as assumed by Helliker & Ehleringer (2000) in their application of the Gat–Bowser formulation. Even though xylem water from the outermost lateral vein was noted to have the highest enrichment among the lateral veins (Fig. 1), this enrichment was still lower than the enrichment of leaf water from a leaf segment at the same vicinity (Fig. 3), after correcting for the humidity difference in Figs 1 and 3. The lower enrichment of vein water in maize, compared to the enrichment of leaf water from the intercostal tissues, has also been noted by Smith, Ziegler & Lipp (1991). This suggests that the relative effects of advection and diffusion, the main feature of the Péclet model, need to be incorporated into the ‘string-of-lakes’ model, as proposed by Gan et al. (2002) and attempted by Farquhar & Gan (2003).

Bulk leaf water

In our experiments, the bulk leaf water of maize leaves was invariably less enriched than ΔC (Fig. 2). In contrast, Helliker & Ehleringer (2000) observed that bulk leaf water in grass species can be considerably more enriched than ΔC. We suspect that the discrepancy between Δb and ΔC in monocotyledonous leaves might be species specific and dependent on leaf length. The study carried out by Helliker & Ehleringer (2000) includes grasses that are only 30–80 mm long whereas the maize leaves in our sampling are 550–900 mm long. A longer blade demands larger and more xylem vessels at the leaf base for faster conduction and higher water carrying capacity. These large vessels are enveloped in layers of parenchyma sheath cells to form large bundle sheaths. The latter are in turn accompanied by several layers of undifferentiated collenchyma cells usually developed on the abaxial side to form a distinct ridge for mechanical support. The bundle sheath parenchyma and vein rib collenchyma are compactly arranged with negligible intercellular air spaces for evaporative enrichment. Accordingly, longer leaves with bigger vein ribs would be expected to have a larger proportion of weakly enriched water in the ground tissues of the vein rib. Indeed, the proportion of water associated with the midrib of maize in the present experiments was 0.430 ± 0.013 of the total leaf water by gravimetric analysis. This value is about three times higher than that associated with the primary veins of cotton leaves (Gan et al. 2002). The water pool from the ground tissues of the vein ribs, denoted ground tissue capacitance by Gan et al. (2002) and Farquhar & Gan (2003), is likely to be enriched to the same extent as the vein xylem water. It thus resembles the ‘vascular pool’ of the two-pool model (Leaney et al. 1985) and is one reason for the lower enrichment of bulk leaf water compared to the Craig–Gordon prediction. It follows that in extracting leaf water for isotopic analysis, whole leaf blades should be sampled, together with a quantification of the vein and ground tissue water fraction (capacitance) by gravimetric analysis. In this work, vacuum distillation of leaf water is shown to be an ideal method for large sample size with a minimum volume of 50 µL. For any volume less (for example in bipinnate leaves), direct pyrolysis of fresh leaf as described by Gan et al. (2002) may be a better approach.

In comparison with leaves at high humidity (Fig. 2), leaves exposed to low humidity consistently showed a smaller proportion of non-enriched bulk leaf water (represented by 1 − ΔbC) despite having higher leaf transpiration rates (Table 1). This result is in conflict with the Péclet model that predicts an increasing value of 1 − ΔbC with increasing transpiration rate. A possible explanation for this anomalous observation will be discussed later. [Note added in proof: the calculations in the present paper were carried out based on a Kinetic fractionation factor of 1.0285. Recent measurements show that this factor should be 1.0319 (Cappa C.D., Hendricks M.B., DePaolo D.J. & Cohen R.C. Isotopic fractionation of water during evaporation. Journal of Geophysical Research (in press)). With this change the anomaly is reduced.]

Enrichment patterns of leaf water and dry matter at different humidities

The magnitudes and spatial patterns of the 18O enrichment of leaf water and dry matter in maize leaves vary with humidity (Fig. 3), consistent with the observations in cotton leaves (Gan et al. 2002). Low humidity leaves show a much larger range of isotopic composition, and the 18O content rises more steeply on approaching the leaf tip. At high humidity, there is little increase in the 18O content of leaf water near the terminus of the water flow. Such variation with humidity in the patterns of isotopic enrichment resembles the general form depicted by the ‘string-of-lakes’ (Fig. 7, Gan et al. 2002), ‘desert river’ and the Farquhar–Gan models (Figs 4 & 7, Farquhar & Gan 2003).

Isotopic enrichment in leaf water will be transferred to leaf organic material due to the exchange of carbonyl oxygen with water, resulting in a 27‰ enrichment of the organic oxygen compared to water at equilibrium (Epstein, Thompson & Yapp 1977; Sternberg & DeNiro 1983). However, the slope of isotopic variation of leaf dry matter along the leaf blade is found to be around 0.4 of that observed for leaf water. We attribute this to the dry matter being a mixture of current photosynthate and older material, for example cellulose. The current photosynthate presumably has an enrichment varying one-to-one with leaf water enrichment. The sucrose used for cellulose formation during the early leaf developmental stage was transported from other mature leaves. This imported sucrose represents the integrated average isotopic content of photosynthates formed over the entire blade of mature leaves. Consequently, the isotopic gradient of leaf dry matter should be smaller than that of leaf water, giving the observed decreasing trend of Δom − Δlw along the leaf blade (Fig. 3).

Quantitative assessment of the ‘string-of-lakes’ model and that converted into a ‘desert river’ system

The ‘string-of-lakes’ model predicts a progressive enrichment of leaf water along the path of water flow from base to tip, and despite this isotopic variation, the average enrichment across the full leaf length in such a model is expected to be same as ΔC. A mathematical formulation of this model with discrete evaporating elements has been provided by Gat & Bowser (1991). For application to leaves, the leaf blade would have to be divided into a finite number of discrete evaporating elements (Helliker & Ehleringer 2000). As isotopic enrichment at any point along the water pathway is sensitive to the number of evaporating elements (Gan et al. 2002), we have chosen three, seven and 20 of such elements in the computation of the Gat–Bowser formulation for comparison with our observed data (Fig. 4). At low humidity, relatively good agreement with the observed ΔlwM was obtained when three evaporating elements were assumed. Theoretical plots with seven or 20 evaporating elements tend to overestimate the extent of enrichment at the leaf tip while underestimating it near the base. At high humidity, none of the Gat–Bowser theoretical plots could accurately predict the observed enrichment along the entire leaf length. Though the enrichment pattern of observed ΔlwM follows the predicted trend, the extent of leaf water enrichment is consistently lower than that predicted for most part of the leaf blade, especially towards the tip.

Figure 4.

Comparison of the measured ΔlwM with the ‘string-of-lakes’ model (Gat & Bowser 1991) for discrete evaporating elements (3, 7 and 20 illustrated here), and the ‘desert river’ model (Eqn 3) for continuous and non-discrete evaporative sites. Δlw refers to the leaf water enrichment of maize leaf segments (5 cm) and ΔM is the maximum enrichment possible according to Eqn 4. There are four replicates of leaf blades in each humidity treatment, two of which have their midrib vein removed (○). Air temperature was 30 °C and the vapour pressure deficits of air at low (RH 34%) and high humidity (RH 75%) were 2.70 and 1.07 kPa, respectively, giving a corresponding ea/ei of 0.268 and 0.580. Values of e+ = 8.4‰, ek = 25.2‰ and Δv = −4.5‰ were used.

In contrast to a series of interconnected lakes, a desert river continually loses water by evaporation. The latter system was first described by Fontes & Gonfiantini (1967), cited in Gat & Bowser (1991) and improved by Farquhar & Gan (2003) for application to leaves (Eqn 3). Using Eqn 3, overestimation of ΔlwM was observed, especially at the distal end of the blade and more so at high humidity (Fig. 4). The curve given by Eqn 3 closely resembles the Gat–Bowser plot with 20 evaporating elements assumed. This is expected since Eqn 3 describes a water system with an infinite number of evaporating elements. Figure 4 illustrates that along the entire leaf blade of maize, the observed leaf water enrichment was always lower than that predicted either by the Gat–Bowser formulation or Eqn 3, and the disparity from theoretical prediction appears to be larger at high humidity than at low humidity. This disparity is consistent with that in the isotopic enrichment of bulk leaf water from whole leaves. To account for the lower enrichment of leaf water, ground tissue capacitance and radial Péclet effects need to be considered in conjunction with the ‘desert river’ model. Analytical solutions for such treatments have been provided (Farquhar & Gan 2003). Before the Farquhar–Gan model can be applied for comparison with our experimental data, we need to estimate the longitudinal and radial Péclet numbers.

Estimate of longitudinal Péclet number from anatomical dimensions

Considering an area of the entire strip of a maize leaf blade between adjacent lateral veins s metres apart and with a constant transpiration rate, E, Farquhar & Gan (2003) showed that the longitudinal Péclet number (Pl) in the longitudinal xylem can be expressed as

image(9)

where lm is the leaf length, ax the cross-sectional area of the vein, C the molar concentration of water (55.5 × 103 mol m−3), D the diffusivity of H218O in water (2.66 × 10−9 m2 s−1). Strictly, ax refers to the cross-sectional areas of the xylem vessels responsible for the longitudinal water flux from the leaf base to the tip. For a wheat leaf, it was reported that longitudinal water flow occurs in both the lateral and intermediate veins (Kuo, O’Brien & Canny 1974), whereas Altus & Canny (1985) concluded that the lateral veins are fully responsible for the longitudinal water transport with the intermediate veins forming part of the reticulation system. To obtain an estimate of Pl, both cases of longitudinal transport will be considered. The anatomical dimensions required for the computation of ax and Pl are given in Table 2 for leaves of maize and wheat, and the results are summarized in Table 3. In maize, Pl is of the order of 107 regardless of the ambient humidity and the means of longitudinal transport, whereas wheat has Pl of the order of 105. It should be noted that although the choice of Pl value, for a given humidity, could influence the shape of a plot of ΔxM versus l/lm, this plot will become almost identical for Pl of the order of 104 and above (Fig. 7, Farquhar & Gan 2003). Should the effective Pl be close to the estimate of Pl given in Table 3 where Pl is generally large, then Eqn 6 would be simplified (Farquhar & Gan 2003) to

Table 2.  Anatomical dimensions of maize and wheat leaves
 MaizeWheat
  1. Measurements of interveinal distance and diameters of xylem vessels were made at several positions along the leaf blade, from scanning electron microscopic prints for maize, and from hand sections for wheat. All data on wheat were obtained from Altus & Canny (1985) and Altus, Canny & Blackman (1985).

Blade length (m)  0.75 0.35
Distance between lateral veins (mm)  1.5–2.0 0.75–1.0
  1.7 (average) 0.8 (average)
Distance between intermediate veins (mm)  0.10–0.13 0.25
  0.12 (average) 
Number of intermediate veins between two
lateral veins
 13 2
Diameter of the largest vessel in a lateral
vein (µm)
 15–5015–40
 30 (average)26 (average)
Diameter of the largest vessel in an intermediate
vein (µm)
  5–10 7–10
  8 (average) 8.5 (average)
Number of such large vessels in a lateral vein  2–3 2–3
Number of such large vessels in an intermediate vein  2–3 3–4
Table 3.  Estimate of longitudinal Péclet number, Pl for leaves of maize and wheat
 MaizeWheat
Low humidityHigh humidity
  1. With reference to the anatomical dimensions in Table 2, Pl was calculated using Eqn 9 for two possible kinds of longitudinal water transport. Transpiration rate of maize leaves was obtained from gas exchange measurements whereas that of wheat leaves was from Kuo et al. (1974) as cited by Altus et al. (1985). The vapour pressure deficits of air at low (RH 34%) and high humidity (RH 75%) were 2.70 and 1.07 kPa, respectively.

  2. As an example of how ax and PM were calculated, we take the case of maize at low humidity.

  3. For longitudinal transport by lateral veins only,

  4. inline image (where 2.5 is the average number of large vessels in the lateral or intermediate vein)

  5. inline image

  6. For longitudinal transport by lateral and intermediate veins,

  7. inline image

  8. inline image

Transpiration rate, E (mmol m−2 s−1)9.05.01.7
Longitudinal transport by lateral veins only
 Cross-sectional area, ax × 10−9 m21.771.771.33
 Pl3.3 × 1071.8 × 1078.2 × 105
Longitudinal transport by lateral and
intermediate veins
 Cross-sectional area, ax × 10−9 m23.403.401.72
 Pl1.7 × 1070.9 × 1076.3 × 105
image(10)

We wish to emphasize that our estimate of Pl using the anatomical dimensions of the parallel veins (Tables 2 & 3) assumes that longitudinal advection and diffusion occur only in the longitudinal xylem. Farquhar & Gan (2003) have, however, highlighted that longitudinal diffusion should also occur in the lamina, although it is yet to be incorporated in the model equation. As longitudinal back diffusion is likely to be more extensive in the lamina than in the xylem, Pl should realistically be smaller than the estimate based on the anatomical dimensions of parallel veins. If the effect of this is to decrease Pl greatly from the xylem-based anatomical estimate, the simplified solution given in Eqn 10 will not hold.

Estimate of radial Péclet numbers from bulk leaf water measurements

We wish to reiterate that while the Pl value could determine the shape of the plot of ΔxM versus l/lm, it does not affect the modelled average enrichment of leaf water across the entire blade. Rather, the discrepancy of the bulk leaf water enrichment from the Craig–Gordon prediction (represented by ΔbC) is dependent on the total radial Péclet number (Pr), the lamina radial Péclet number (P), the veinlet radial Péclet number (Prv), and the fractions of bulk leaf water represented by major veins (φx), lamina mesophyll (φl) and veinlets (φv), as follows (Farquhar & Gan 2003):

image(11)

where φx + φl + φv = 1 and Pr = P + Prv. By gravimetric analysis, the leaf water fraction associated with the midrib of maize leaves (φx) was measured to be 0.43 ± 0.013. The proportion represented by minor veins such as intermediate veins (φv) was estimated as approximately 0.01 based on the anatomical dimensions of these veins (Table 2). This latter value does not include the contribution from the ground tissues of these veins which is, nevertheless, expected to be insignificant compared to that from the ground tissues of the midrib.

To determine Pr, we compare the spatial variation of ΔxM of the midrib and of the marginal lateral vein (from Fig. 1) with plots of ΔxM versus l/lm for different values of Pr using Eqn 6(Fig. 5). At Pl = 107 and 100 (Fig. 5a & b), none of the theoretical plots could describe well the spatial variation of xylem enrichment for these major veins. At Pl = 10 (Fig. 5c), the isotopic variation of the marginal lateral vein compares well with the plots having Pr = 0.7 and 0.8, whereas that for the midrib only fitted well over the last third of its water pathway with Pr = 0.8. The discrepancy with theory of the midrib ΔxM at the initial part of water flow may indicate that Pr is not constant throughout the leaf length. It is striking that the value (10) of Pl obtained from the data fitting of vein xylem water enrichment is so different from that predicted (107) based on the anatomical dimensions of vein xylem. In the next section, the extent of agreement with the xylem-based anatomical estimate of Pl will be further assessed using experimental data on the leaf water enrichment of maize segments.

Figure 5.

Comparison of the measured ΔxM of the midrib (○) and the marginal lateral vein (▪) with the Farquhar–Gan model (Eqn 6) at 50% relative humidity (air temperature, 30 °C; VPD of air, 2.12 kPa; ea/ei = 0.399; h′ = 0.378 according to Eqn 5). Δx refers to the vein xylem water enrichment, ΔM the maximum enrichment possible according to Eqn 4 and l/lm is the relative distance from leaf base with lm being the maximum length of individual vein. The modelled curves for different radial Péclet number (Pr) are shown for Pl = 107 (a); Pl = 100 (b); and Pl = 10 (c). Values of e+ = 8.4‰ and ek = 25.2‰ were used.

With Pr estimated to be around 0.8 from the enrichment of xylem water in the major veins at 50% RH, we first assumed that the same Pr value also applies to other humidity treatments in the next step of determining P, the lamina radial Péclet number, from ΔbC using Eqn 11. Since there is no simple analytical expression for P in terms of ΔbC, we solved for P numerically using the mathematical software package, MATHEMATICA. Based on the results of Fig. 2, estimates of P were obtained and are summarized in Table 4. For a constant Pr, the P-values are generally larger at higher humidity, in tandem with the variation of 1 − ΔbC. We note that if φv is taken to be zero instead of 0.01 as estimated, P increases by only 0.01 for both humidities. In view of the small value of φv and its minimal effect on P, one could simplify Eqn 11 to

Table 4.  Estimate of lamina radial Péclet number (P) and total radial Péclet number (Pr) in maize leaves at two humidity levels
 ΔbCEstimate of PEstimate of Pr
Eqn 13Eqn 11
Pr = 0.8
Lower bound
Eqn 14
P = Pr
Upper bound
Eqn 15
P = 0
Special case
Eqn 16
P = 0.5 Pr
  1. The P-values were calculated from ΔbC (as shown in Fig. 2) using Eqn 13 (Farquhar & Lloyd 1993) or Eqn 11 (Farquhar & Gan 2003) for comparison. For the latter, measured values of Pr = 0.8, φx = 0.43 and φv = 0.01 were used, where Pr was obtained from measurements of vein xylem water enrichment (Fig. 5). Alternatively, Pr values can be estimated from Eqn 14 (lower bound), Eqn 15 (upper bound) and Eqn 16 (special case where Pr = 2P). Here, Pr values were obtained with φx = 0.43 and φv = 0. The symbol Δb refers to the 18O isotopic composition of bulk leaf water for the entire blade whereas ΔC is the predicted enrichment according to the Craig–Gordon model. The vapour pressure deficits of air at low (RH 34%) and high humidity (RH 75%) were 2.70 and 1.07 kPa, respectively.

Low humidity0.716 ± 0.0670.71 ± 0.220.16 ± 0.290.49 ± 0.151.08 ± 0.610.64 ± 0.21
High humidity0.604 ± 0.0181.11 ± 0.070.68 ± 0.100.75 ± 0.052.54 ± 0.751.01 ± 0.07
image(12)

where φx + φl = 1 and Pr = P + Prv.

The definition of P in the Farquhar–Gan model is similar to the leaf Péclet number in the earlier Péclet model (Farquhar & Lloyd 1993). However, the relationship of this Péclet number (P) to ΔbC will be slightly different for the two models. In the earlier Péclet model, the vein water is assumed to be unenriched and to constitute a negligible fraction of the total leaf water, such that the bulk leaf water is mainly water from the lamina mesophyll and

image(13)

Comparing the two approaches of calculating P (Eqns 11 and 13), that from Eqn 11 invariably gives smaller values, with the difference here being as much as 0.55 (Table 4). This is expected as the Farquhar–Gan model takes into account the capacitance in the ground tissues of major vein ribs that would have enrichment similar to the xylem water, and lower than that of the lamina mesophyll water. With the shortfall of leaf water enrichment from ΔC partly attributed to ground tissue capacitance in the vein ribs with low degree of enrichment, a smaller P-value should be obtained.

For cases where spatial variation of xylem water enrichment is not available for Pr determination, one could still estimate the possible range of Pr from Eqn 12. By assuming Prv to be zero such that Pr = P, a lower bound on Pr can be obtained from

image(14)

An upper bound on Pr can also be estimated by allowing P to approach zero such that

image(15)

In the case of P = Prv such that Pr = 2P,

image(16)

From ΔbC and φx measurements, the lower (Eqn 14) and upper bound (Eqn 15) values of Pr, together with Pr (Eqn 16) in the special case of P = Prv, were calculated for low and high humidity treatments and are presented in Table 4. As expected by Farquhar & Gan (2003), the total radial Péclet number (Pr) is much smaller in magnitude than the longitudinal Péclet number, with a maximum Pr value of 2.5. The range of lamina radial Péclet number (P) is even smaller, with a possible maximum of 0.75, as dictated by Eqn 14 where Pr = P.

Quantitative assessment of the Farquhar–Gan model

With the Pl and Pr estimated to be around 107 (based on the anatomical dimensions of vein xylem) and 0.8, respectively, and P as 0.16 (low humidity) and 0.68 (high humidity), we proceed to obtain theoretical plots of Δ/ΔM versus l/lm based on the Farquhar–Gan model and compare these with the measured ΔlwM of maize leaf segments (Fig. 6). Only results with the midrib intact are represented based on the notion that vein water is an intrinsic component of the leaf water enrichment (Gan et al. 2002). With P greater than zero, Δl/ΔM takes a value between ΔxM and ΔeM, with the latter being the highest throughout the leaf length. Measured values of ΔlwM should be a weighted mean of Δx/ΔM and Δl/ΔM according to the water fraction associated with the major veins, φx, such that

Figure 6.

Comparison of the measured ΔlwM with the Farquhar–Gan model (Eqns 6–8, 17) at two levels of humidity. Round symbols with interpolated line represent true measurements of the enrichment of leaf water (Δlw) of maize leaf segments (5 cm). For each humidity treatment, two replicates of leaf blades with the midrib intact are presented. ΔM is the maximum enrichment possible according to Eqn 4 while Δx, Δlw, Δl and Δe are the predicted enrichment of vein xylem water, bulk leaf water, lamina mesophyll water, and leaf water at the sites of evaporation, respectively. Panels (a) and (b) assume that all lateral veins terminate at the leaf tip while (c)–(f) consider tapering of the leaf blade towards the tip, with the first vein (outermost) terminating at l/lm = 0.6 and the midrib terminating at the leaf tip. For curves (c)–(f), 80 lateral veins were assumed during calculation to smoothen the curve for clarity. Different longitudinal Péclet (Pl) numbers were used for (e) and (f), as indicated. At low humidity (RH 34%), VPD of air = 2.70 kPa, ea/ei = 0.268 and h′ = 0.243; at high humidity (RH 75%), VPD of air = 1.07 kPa, ea/ei = 0.580 and h′ = 0.566. Values of e+ = 8.4‰ and ek = 25.2‰ were used.

image(17)

Equation 17 is similar to Eqn 12, with the former describing varying enrichment along the leaf length whereas the latter describes the spatial average of enrichment over the entire leaf. Since the value of φx in maize is estimated to be 0.43, ΔlwM should lie somewhere near the midpoint of the two lines of Δx/ΔM and Δl/ΔM, as shown in Fig. 6.

At Pl = 107 (Fig. 6a & b), the modelled isotopic pattern of enrichment along the leaf length does not reflect the observed pattern, especially at high humidity. There is a consistent underestimation of the leaf water enrichment at a relative distance of 0.4–0.9 from the leaf base but an overestimation of the same near the leaf tip.

The observation of higher leaf water enrichment at l/lm of 0.4–0.9 is probably a result of tapering of the leaf blade towards the tip. The maize leaf has about eight lateral veins on each side of the midrib and the interveinal distance remains relatively constant throughout the leaf length. The outermost lateral vein terminates at a relative distance of about 0.6 from the base whereas the midrib terminates at the leaf tip. In contrast, the modelled curves plotted in Fig. 6a & b assumed that all the lateral veins terminate, and reach maximum enrichment, at the tip. Consequently, the observed enrichment of bulk water in a leaf segment would be higher than predicted as xylem water in the marginal veins approached maximum enrichment ahead of that in the midrib. When the eight lateral veins were modelled to terminate, first at l/lm of 0.6 for the marginal vein, and equidistant apart thereafter for the remaining laterals until the midrib terminates at the tip, the agreement with observed values was improved (Fig. 7), where the ΔxM curve now represents the enrichment average of xylem water in the 16 lateral veins and the midrib. Interestingly, the modelled curves become ‘zig-zag’ from where tapering begins at l/lm of 0.6. Such fluctuations arise due to the mathematical treatment of summing up a small number of lateral veins that dwindles as the leaf tapers. In reality, diffusion of H218O should smooth out any sharp changes of isotopic gradients. When the number of lateral veins was assumed to be 80 in calculating ΔxM, a smooth curve was obtained (Fig. 6d). Thus, for clarity and a more realistic representation, the assumption of 80 lateral veins was applied in plotting the modelled curves in Fig. 6c–f.

Figure 7.

Comparison of the measured ΔlwM with the new model (Eqns 6–8, 17) after taking into account the tapering of the leaf blade towards the tip. In calculating ΔxM, 16 lateral veins were assumed present, with the first vein (outermost) terminating at llm = 0.6 and the midrib terminating at the leaf tip. High humidity treatment is illustrated, with the experimental conditions and symbols as described in Fig. 6. Values of Pl = 107, Pr = 0.80, and P = 0.68 were used.

After correcting for the tapering of the leaf blade (Fig. 6c & d), the modelled curve of ΔlwM follows the leaf water measurements more closely, except for those near the leaf tip. To bring the predicted enrichment at the leaf tip down closer to the observed values, Pl would need to be reduced to 104 at low humidity and 100 at high humidity. As illustrated in Fig. 6e & f, a good fit of the measured to the modelled curves is attained, especially near the leaf tip. The radial Péclet numbers obtained by measuring the vein xylem and bulk leaf water enrichment (Table 4, Eqn 11: low humidity, Pr = 0.8 and P = 0.16; high humidity, Pr = 0.8 and P = 0.68) produce theoretical curves that describe well the measured ΔlwM of leaf segments (Fig. 6e & f). In the absence of measurements of vein xylem enrichment for the prediction of Pr, Eqn 16 is observed to predict the values of Pr and P better than Eqns 14 and 15 at low humidity whereas Eqn 14 performs best at high humidity (Table 4).

It is important to note that although Pl of 104 (RH 34%) and 100 (RH 75%) were needed to fit the measurements of leaf water enrichment (Fig. 6e & f), only a Pl value of 10 describes well the measurements of vein xylem water enrichment at RH 50% (Fig. 5). We cannot provide a specific explanation for this discrepancy but one possible cause might be the influx of xylem water into the phloem during sucrose loading (Hall & Milburn 1973). This implies that the water path of xylem water may not necessarily reach its terminus at the leaf tip, as assumed in the theoretical lines of Fig. 5. Other explanations for the discrepancy of the effective Pl from the xylem-based anatomical estimate will be discussed in the next section.

Possible explanations for the deviation of best-fit Pl from the anatomical estimate

To cater for the lower than expected enrichment at the distal end of the leaf blade, the best-fit Pl values need to be 3 (low humidity) or 5 (high humidity) orders of magnitude lower than the estimate based on the anatomy of vein xylem. However, this discrepancy of Pl could be effectively just one order of magnitude for high humidity treatment since ΔxM at the leaf tip is insensitive to changes in Pl once Pl > 1000 (Fig. 8).

Figure 8.

Modelled sensitivity of terminal ΔxM to longitudinal Péclet number (Pl) at two levels of humidity. Terminal ΔxM was calculated from Eqn 6 with l = lm, Pr = 0, e+ = 8.4‰ and ek = 25.2‰. At low humidity, ea/ei = 0.268 and h′ = 0.243; high humidity, ea/ei = 0.580 and h′ = 0.566.

Tapering of veins towards the leaf tip (as distinct from the tapering of the leaf blade discussed earlier) has not been accounted for in the model. For the case in which vein tapering maintains advection and reduces back diffusion, including this effect would worsen the discrepancy in xylem-based Pl and the effective value.

One possible cause of the lower enrichment at the leaf tip is that the lamina in that vicinity could be cooler than the rest due to the drooping of the long blade at its terminal end and the consequent reduction in light interception. This would make ea/ei at the leaf tip higher than for the rest of the lamina, giving smaller Δx and Δl values at the tip. For the case of the high humidity treatment, bringing the predicted ΔxMand Δl/ΔM closer to the observed at the distal end would require the leaf tip to be cooler, by about 5 °C, than the rest of the lamina. This temperature difference is probably too large in reality. Using an IR imaging scanner, temperature variation along a leaf blade was measured to be 3.5 °C at most, with no clear pattern of variation.

A more probable explanation for the deviation of best-fit Pl from the anatomical estimate lies in the inherent assumption of the latter approach. As mentioned earlier, using the anatomical dimensions of vein xylem to estimate Pl assumes that longitudinal advection and diffusion could only occur in the longitudinal xylem. However, back diffusion of enriched water in the leaf lamina should arise not only in the radial direction but also in the longitudinal direction (Fig. 1d, Gan et al. 2002), as highlighted by Farquhar & Gan (2003). From the theoretical curves depicted in Fig. 6a–d, the large isotopic gradient developing at the tip should lead to a huge longitudinal diffusion flux of H218O within the mesophyll tissue itself, rendering the enrichment at the tip lower and more ‘evenly’ distributed in that vicinity. Longitudinal diffusion in the leaf lamina is likely to be more extensive than in the xylem for two reasons. One is the lower flow velocity in the lamina mesophyll compared to that in the vein xylem. The other is the larger area available for diffusion through the lamina mesophyll, in comparison with the smaller cross-sectional area of the longitudinal xylem vessels. Extensive longitudinal diffusion in the lamina mesophyll might translate to a smaller longitudinal Péclet number that would lead to a better fit of the experimental data.

Although the value of Pl predicted based on the anatomy of vein xylem may not be reliable, predictions of the average enrichment of leaf water for most applications will still be unaffected since the average enrichment of leaf water does not depend on the value of Pl (Farquhar & Gan 2003).

Effects of spatially varying transpiration rate

One implicit but important proposition arising from the Farquhar–Gan model is that the spatial pattern of leaf transpiration rate ought to be characterized concurrently with the isotopic measurements of leaf water for a better understanding of bulk leaf water enrichment. Unfortunately, the work described in this paper was carried out before the development of the model when we did not anticipate the importance of monitoring the transpiration rate variation along a leaf in its natural orientation. As such, these spatial measurements were not meticulously pursued, especially after initial attempts had shown that there was no significant transpiration rate difference between the proximal and distal regions. The preliminary results may have been misleading as measurements were made after the leaves had been ‘straightened’ for full exposure to uniform light.

In the work of Helliker & Ehleringer (2000), the observation of grass species having leaf water enrichment greater than ΔC was unanticipated. However, the authors had the insight of ascribing the higher enrichment to variable transpiration rate, E, along the leaf blade. Applying the Gat–Bowser formulation, they varied E to match the observed isotopic composition of leaf water segments, δlw. They then demonstrated, using the particular pattern of E, that the mean spatial average of δlw predicted over all the segments was higher than ΔC. Farquhar & Gan (2003) have now shown, in theory, that the average enrichment at the sites of evaporation depends on the pattern of water loss along the leaf. For a spatially varying transpiration rate, there are two ways of calculating the average enrichment across the entire leaf. These two approaches may, however, lead to different results. If the average were obtained by applying a weighting based on the cumulative amount of water transpired, the mean enrichment of water at the sites of evaporation should approach ΔC with no dependency on the spatial variation of the transpiration rate. In other words, enrichment of leaf water increases along the leaf length according to the cumulative amount of water transpired. In contrast, the spatial average enrichment at the sites of evaporation over the entire leaf could be larger than, smaller than, or equal to ΔC, depending on the spatial variation of transpiration rate. If transpiration rates are higher towards the leaf base and lower at the tip region, it implies that water is mostly transpired from the lower part of the leaf blade, resulting in a rapid accumulation of enriched water in that region. Thus the remaining distal part of the blade would continue with a highly enriched isotopic signature, and the spatial average of Δe across the entire blade would invariably be greater than ΔC. Similarly, the scenario of low transpiration rate at the basal region and high transpiration rate near the tip would lead to a spatially averaged Δe lower than ΔC. These predictions assume that varying transpiration rate has no effect on the spatially uniform distribution of the isotopic composition (Δv) of the vapour above the leaf, especially in a well-ventilated environment where there is forced convection. Uniform transpiration rates across the leaf should give a spatially averaged enrichment (at the sites of evaporation) equivalent to ΔC.

We could not find any direct study on the spatial variation of leaf transpiration rate, except for two indirect assessments based on stomatal conductance (gs) measurements (Meinzer & Saliendra 1997; Buckley & Mott 2000). The former studied the longitudinal variation of A, gs and PPFD along sugarcane leaves (130 cm long) in their natural orientation in the glasshouse. They noted a general increase in A and gs from the base to the tip and attributed it to increasing incident PPFD. On the other hand, Buckley & Mott (2000) observed that at constant PPFD along the entire leaf, gs from the distal half of a wheat leaf (<30 cm long) is lower than that from the proximal half at high humidity, and this difference becomes insignificant at low humidity. In our experiment with maize leaves, the discrepancy between the observed and predicted enrichment of leaf water, 1 − ΔbC, decreases with transpiration rate, opposing the predicted trend of the Péclet model. This anomaly could be attributed to different patterns of transpiration rate variation along the leaf for different humidity treatments. Unfortunately, the response of transpiration rate heterogeneity to humidity has not been characterized in our study or in that of Meinzer & Saliendra (1997) on sugarcane leaves. Stomatal response to light might have different sensitivities at different humidities. Spatial variation of stomatal conductance is expected to be more pronounced for long flagging leaves that intercept light of a wide-ranging intensity than for short, stiff leaves. Another possible cause of the anomaly is that plants grown under different humidities may have differed anatomically. Perhaps the plants grown at high humidity had a higher Péclet number at a particular transpiration rate, than the plants grown at low humidity.

Predicting growth humidity from Δ18O measurements

The oxygen stable isotope composition of plant organic matter can assist in the reconstruction of palaeoclimatic data such as temperature and relative humidity (Gray & Thompson 1976, 1977; Epstein et al. 1977; Burk & Stuiver 1981; Roden & Ehleringer 2000). The present challenge is to tease apart the intertwined signals of growth temperature and humidity imprinted in plant organic matter.

The Farquhar–Gan model predicts that the enrichment pattern of leaf water along the leaf length is largely dependent on humidity and it has been shown that such differences in spatial variation are recorded in the Δ18O of both leaf water and organic matter (Fig. 3). Although the enrichment pattern of leaf dry matter is not as well defined as that for leaf water, the former still retains the strong feature of large Δ18O variation along the full length of the leaf at low humidity. The sensitivity of the Δom range to humidity is within expectations as Δom at the leaf base is representative of the source water signature, independent of the growth humidity, whereas that at the tip reflects the maximum possible enrichment of leaf water that is strongly dictated by humidity. Thus, a good estimate of the prevailing growth humidity could be obtained by studying the slope of the Δ18O variation of leaf dry matter along the leaf length. For the dry matter of maize leaves in this study, the slope is approximately 17.2‰ per leaf full length at 34% RH and 5.7‰ at 75% RH (Fig. 3). This approach is expected to be most effective for fast-growing leaves where leaf expansion to the full length is more likely to occur under similar humidity conditions within a growth season. While the slope of the Δ18O variation of leaf dry matter is humidity-dependent, we could not claim the same for the Δ18O of leaf cellulose, a component not measured in our experiment. We speculate that for a constant growth humidity, the spatial variation of the Δ18O of leaf cellulose is likely to be relatively smaller than that of the leaf dry matter, since the former is expected to represent the integrated Δ18O of photosynthates imported from other mature leaves during the leaf development.

For the reconstruction of past climate, we propose the analysis of the Δ18O increment along the length of leaf macrofossils present in middens (packrat middens in the south-west of America (Long et al. 1990) and stick-nest rat middens in South Australia (McCarthy & Head 2001)) as an alternative method for estimating the atmospheric humidity during the past thousands of years. To explore this potential application, further measurements of modern plant samples (both leaf dry matter and leaf cellulose) at different humidities are required to generate calibration plots, and are beyond the scope of this paper.

CONCLUSION

The Farquhar–Gan model gave good predictions of the variation of leaf water enrichment pattern with humidity, and accounted for the observed average enrichment of bulk leaf water. Applying the new model requires the knowledge of longitudinal and radial Péclet numbers. The longitudinal Péclet number can be calculated from the anatomical dimensions of vein xylem, giving values as high as 107. This estimate is much higher than observed, and reasons for this deviation are discussed. The radial Péclet numbers can be determined from the spatial variation of xylem water enrichment and the average enrichment of bulk leaf water. These numbers, in the range of 0–2.5 in this study, are smaller than the longitudinal Péclet number. Whereas the value of longitudinal Péclet number determines the spatial pattern of Δ18O variation of leaf water along a blade, theory says that it is the radial Péclet numbers that determine the average enrichment of leaf water across the entire blade. However, spatial heterogeneity of leaf transpiration rate could complicate the prediction of bulk leaf water enrichment. One potential application of the Farquhar–Gan model is the reconstruction of past atmospheric humidity from the slope of the Δ18O variation of leaf dry matter along the length of leaf macrofossils, teasing apart the intertwined relationship of growth temperature and humidity recorded in bulk organic matter.

ACKNOWLEDGMENTS

We are grateful to Todd Dawson for suggesting the use of middens in testing our gradient-based approach for humidity prediction, and to Brent Helliker and Tom Buckley for useful discussions on the observation of variable transpiration rates. The technical assistance of Katherine Gosling in leaf sampling, and the technical support rendered by the Electron Microscopy Unit (Australian National University) are much appreciated.

APPENDIX

List of symbols

  • δs   oxygen isotopic composition of source water with respect to Vienna Standard Mean Ocean Water (VSMOW)

  • δv   oxygen isotopic composition of atmospheric watervapour with respect to VSMOW

  • Δb  oxygen isotopic composition of bulk water from the whole leaf blade, relative to source water

  • ΔC  oxygen isotopic composition of leaf water relative to source water, as defined by the modified Craig–Gordon equation (Eqn 1)

  • Δe   oxygen isotopic composition of leaf water at the sites of evaporation, relative to source water

  • Δl   oxygen isotopic composition of lamina mesophyll water, relative to source water

  • Δlw   oxygen isotopic composition of leaf water from small leaf segments, relative to source water

  • ΔM   the maximum possible 18O enrichment of leaf water, relative to source water

  • Δom oxygen isotopic composition of leaf organic matter, relative to source water

  • Δv   oxygen isotopic composition of atmospheric water vapour, relative to source water

  • Δx   oxygen isotopic composition of xylem water in the major veins, relative to source water

  • e+   oxygen isotope equilibrium fractionation factor

  • ek   oxygen isotope kinetic fractionation factor

  • φx   mass fraction of bulk leaf water represented by water in the major veins and in the ground tissues of these veins

  • φl   mass fraction of bulk leaf water represented by lamina mesophyll water

  • φv    mass fraction of bulk leaf water represented by water in the veinlets

  • ax   cross-sectional area of the longitudinal xylem

  • C   molar density of water (55 × 103 mol m−3)

  • D   diffusivity of H218O in water

  • E   leaf transpiration rate (mol m−2 s−1)

  • ea   ambient water vapour pressure (mbar)

  • ei   water vapour pressure in the intercellular spaces (mbar)

  • h   relative humidity at the leaf temperature (equal to ea/ei)

  • h′   a parameter approximately equal to h and as defined in Eqn 5

  • k   a parameter incorporating h′ and Pr and defined as inline image

  • l   longitudinal length along the main axis of the leaf, measured from the base

  • lm   total length of a leaf along the main axis

  • P   lamina radial Péclet number

  • Prv  veinlet radial Péclet number

  • Pr    total radial Péclet number

  • Pl   longitudinal Péclet number along the main axis of the leaf

  • s   interveinal distance

Ancillary