We present field observations of carbon isotope discrimination (Δ) and internal conductance of CO2 (gi) collected using tunable diode laser spectroscopy (TDL). Δ ranged from 12.0 to 27.4‰ over diurnal periods with daily means from 16.3 ± 0.2‰ during drought to 19.0 ± 0.5‰ during monsoon conditions. We observed a large range in gi, with most estimates between 0.04 and 4.0 µmol m−2 s−1 Pa−1. We tested the comprehensive Farquhar, O'Leary and Berry model of Δ (Δcomp), a simplified form of Δcomp (Δsimple) and a recently suggested amendment (Δrevised). Sensitivity analyses demonstrated that varying gi had a substantial effect on Δcomp, resulting in mean differences between observed Δ (Δobs) and Δcomp ranging from 0.04 to 9.6‰. First-order regressions adequately described the relationship between Δ and the ratio of substomatal to atmospheric CO2 partial pressure (pi/pa) on all 3 d, but second-order models better described the relationship in July and August. The three tested models each best predicted Δobs on different days. In June, Δsimple outperformed Δcomp and Δrevised, but incorporating gi and all non-photosynthetic fractionations improved model predictions in July and August.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
A substantial body of literature describing a linear relationship between leaf carbon isotope discrimination (Δ) and the ratio of internal to atmospheric CO2 partial pressure (pi/pa) has accumulated in the last three decades (Farquhar et al. 1982b; Brugnoli et al. 1988; Farquhar, Ehleringer & Hubick 1989; Ehleringer, Phillips & Comstock 1992; Brugnoli & Farquhar 2000). The pi/pa ratio is useful because it succinctly describes the dominant physical and biochemical constraints to photosynthesis. Similarly, the linear relationship between Δ and pi/pa observed in previous studies emphasizes the importance of stomatal conductance and biochemistry in Δ. The full model of Δ developed by Farquhar et al. (1982) also accounts for other factors such as internal conductance of CO2 from stomatal cavities to sites of carboxylation (gi) and apparent isotopic fractionations associated with the decarboxylation processes of day respiration and photorespiration (Δef), as well as other diffusion-related fractionations. Recent evidence suggests that gi and Δef are sensitive to environmental factors that vary diurnally (Bernacchi et al. 2002; Ghashghaie et al. 2003; Warren, Livingston & Turpin 2004), but their role in the variation in Δ observed in a field setting remains poorly understood.
The influence of environmental factors on Δef is less well known. Temperature and light have been shown to influence day respiration and photorespiration, both of which affect CO2 evolution within a leaf (Brooks & Farquhar 1985; Kozaki & Takeba 1996; Atkin et al. 2000, 2005). The apparent fractionation associated with day respiration (e) and photorespiration (f) are each the result of biochemical reactions that may be subject to environmental control (Ghashghaie et al. 2003). A consistent enrichment of 6‰ in the dark respired 13C/12C ratio (δ13Cresp) of CO2 compared to sucrose of droughted and control Phaseolus leaves has been observed (Duranceau et al. 1999). Such respiratory enrichment has been shown to depend on species and on plant water status (Ghashghaie et al. 2001), temperature (Tcherkez et al. 2003), and light exposure (Barbour et al. 2007a). Estimates of e have largely been inferred from studies of dark respiration, but recent evidence suggests these dark respiration fractionations may not be representative of day respiratory fractionation (Tcherkez et al. 2008). Field observations of the diurnal patterns of the cumulative fractionation associated with respiratory and photorespiratory processes, estimated here in Δef, may allow us to better understand the influence of environmental factors on this component of Δ.
In recent years, advances in optical systems utilizing tunable diode laser spectroscopy (TDL) have simplified high-frequency measurements of the abundance of individual isotopologues 13C16O2, 12C16O2 and 12C18O16O in ecosystem studies (Bowling et al. 2003; Griffis et al. 2004; McDowell et al. 2008a) and leaf-scale studies in greenhouse settings (Barbour et al. 2007a,b) Similar TDL leaf-scale measurements can now be attempted in a field setting. The objectives of this study were to (1) examine the temporal variation in Δ, δ13Cresp, gi and Δef under ambient field conditions; (2) test the hypothesis that gi varies across the day; (3) test the hypothesis that Δ varies linearly in response to shifts in pi/pa under field conditions; (4) test the influence of gi in a comprehensive leaf model of Δ; and (5) test the predictive capabilities of three models: the comprehensive Farquhar et al. (1982) model of Δ (Δcomp), a recently suggested amendment to Δcomp (Δrevised; Wingate et al. 2007) and the simplified form of the comprehensive model (Δsimple). We used a combined TDL-infrared gas analyser (IRGA) system to obtain high-frequency field measurements of leaf gas exchange synchronized with online isotopic measurements, similar to those used in previous greenhouse studies (Barbour et al. 2007a). Previous work has demonstrated substantial diurnal variation in leaf discrimination in diverse field settings including tropical forest (Harwood et al. 1998) and mesic conifer forest (Wingate et al. 2007). We report ∼20 Δ measurements per hour over diurnal periods during both dry and wet seasons from a semi-arid woodland.
The field site was located on Mesita Del Buey in Los Alamos, New Mexico, USA (35°50′N, 106°16′W; elevation 2140 m) in a piñon-juniper woodland (Pinus edulis Engelm. and Juniperus monosperma Engelm. Sarg., respectively) dominated primarily by juniper and understorey grasses and forbs (Breshears 2008; McDowell et al. 2008b). This semi-arid region typically has a bimodal precipitation regime, with substantial winter snowfall (October–April), followed by a dry period (May–June) and monsoonal precipitation from July through early September (Breshears 2008). Precipitation at our site in 2006 totaled 119 mm in winter and 224 mm in summer. Soils on the site are Typic Haplustalfs and Typic Ustochrepts (Davenport, Wilcox & Breshears 1996).
Leaf gas exchange measurements
We measured diurnal (0600–1900 h) leaf gas exchange from the bottom third of the canopy on two juniper trees on 12 June 2006, two different juniper trees on 11 July 2006 and a single juniper on 14 August 2006. We coupled a TDL (TGA100A; Campbell Scientific Inc., Logan, UT, USA) to a portable photosynthesis system (Li-Cor 6400; Li-Cor Biosciences, Lincoln, NE, USA) fitted with a conifer chamber (Li-Cor 6400-05) to quantify the concentration of CO2 and its isotopologues 13C16O2 and 12C16O2 in gas entering and exiting the leaf chamber, herein referred to as the reference and sample gas streams (i.e. Barbour et al. 2007a). We supplied atmospheric air via a 50 L buffer volume to the Li-Cor 6400, which recorded the CO2 and water vapour concentration of the reference and sample gas every 10 s. These same gas streams were dried to a constant low humidity and plumbed directly into the TDL using ultra-low porosity tubing (Synflex type 1300 ¼ in. diameter; Saint Gobain Performance Plastics, Northboro, MA, USA) wherein the TDL measured the CO2 isotopologues 13C16O16O and 12C16O16O at a rate of 500 Hz. These 500 Hz data were then averaged down to 10 Hz, and all means were calculated from the 10 Hz data. Our 3 min TDL measurement cycle consisted of two reference tanks and the reference and sample gas streams, each measured for 45 s, from which we calculated means of isotopologue concentrations over the last 15 s of each inlet cycle. We combined these TDL data with IRGA-generated data after incorporating the 33 s lag between the two instruments.
We used a Li-Cor conifer chamber to maximize leaf area and allow natural light interception on the scalelike juniper foliage, regulating the chamber flow rate between 250 and 500 µmol s−1 to maintain a sufficient CO2 drawdown and control chamber humidity. We attempted to maintain CO2 drawdown ≥40 µmol CO2 mol−1 air within the leaf chamber. Under moderate conditions, chamber temperature was unregulated, but under conditions of high ambient air temperature (>35 °C) and solar radiation, the IRGA block temperature control was engaged to control leaf temperature below 35 °C, as measured by energy balance. On 12 June, we collected data from six leaf areas diurnally and from two leaf areas at night. On 11 July, we collected data from five leaf areas diurnally and two leaf areas during dark measurements. In both June and July, each leaf area was measured for 30 min to an hour and leaves were typically measured more than once each day. Finally, on 14 August, we collected all data from one leaf area diurnally during a 7 h period, and one leaf area during dark measurements. The isotopic signature of nocturnal respiration (δ13Cresp) was measured immediately following daylight measurements and beginning when ambient photosynthetic photon flux density (PPFD) fell below 30 µmol photons m−2 s−1 and foliage exhibited net CO2 efflux. To achieve a true dark measurement, we applied a heavy shade cloth over the leaf chamber to reduce PPFD to zero and waited for stable chamber conditions (e.g. leaf temperature and respiration rate), which occurred within 5 min after the shade cloth was applied. We also determined the carboxylation capacity of these juniper trees on 22 June and 23 July 2007 using assimilation (A) responses to changes in substomatal CO2 concentration (A/pi). We collected these data using a Li-Cor 6400 fitted with a chamber light source (Li-Cor 6400-02B). We measured pre-dawn and midday xylem water potential (ψw) on 5 to 10 nearby juniper trees on each measurement day using a Scholander-type pressure bomb (PMS Instruments Co., Corvallis, OR, USA; McDowell et al. 2008b).
The working standard (WS) calibration tanks used during our diurnal measurements were calibrated against World Meteorological Organization (WMO)-certified standard tanks (541.67 µmol CO2 mol−1 air, δ13C = −16.16‰ and 350.34 µmol CO2 mol−1 air, δ13C = −8.39‰) within 24 h of each measurement campaign. The intertank calibration between WMO and WS tanks typically required 2 h to complete. Molar mixing ratios of 12CO2:13CO2 in the WS tanks used in the June campaign were 354.04 ± 0.27:3.82 ± 0.003 µmol CO2 mol−1 air (mean ± standard error; n = 11 inter-tank calibrations) and 563.85 ± 0.27:6.09 ± 0.003 µmol CO2 mol−1 air (n = 11). Molar mixing ratios of 12CO2:13CO2 in the WS tanks used in the July and August campaigns were 340.46 ± 0.29:3.67 ± 0.003 µmol CO2 mol−1 air (n = 10) and 518.71 ± 0.08:5.60 ± 0.001 µmol CO2 mol−1 air (n = 6). The WMO-certified tanks were filled and δ13C calibrated at the Stable Isotope Lab (SIL) of the Institute for Arctic and Alpine Research, a cooperating agency of the Climate Monitoring division of the National Oceanic and Atmospheric Administration's Earth Research Laboratory. Measurement variation in the δ13C of a known tank in the TDL measurement mode we used exhibited an SD of 0.06‰ across an hour and 0.20‰ across the day. To account for diurnal instrument drift, the TDL measured the high and low WS tanks during each 3 min cycle, and we calculated the deviation between the measured values and the known values to determine a gain and offset for each isotopologue in each tank being measured (Bowling et al. 2003). These gain and offset values were then applied to all data. The TDL measures the absolute concentration of each isotopologue, so the range of 12CO2 and 13CO2 in each WS tank should span the measurement range. During the three measurement days, our measurements occasionally exceeded the lower end of the total [CO2] in our WS tanks (maximum deviation: 45.7 µmol mol−1). To test that the calibration was valid below the lower tank, we used a WMO traceable standard tank (total [CO2] = 142.86 µmol mol−1, δ13C = −7.96‰) and an additional unknown tank that had a target total [CO2] of 250 µmol mol−1. We measured these two tanks and two WS tanks (344.88 µmol mol−1, −8.16‰ and 548.16 µmol mol−1, −16.42‰) in series. We calculated the total [CO2] and isotope ratio of the unknown tank by calculating the gain and offset values in two ways: (1) using the span between the 142.86 µmol mol−1 tank and the 344.86 µmol mol−1 tank and (2) using the span between the 344.86 µmol mol−1 tank and the 548.16 µmol mol−1 tank measurements. The unknown tank was calculated to have a total [CO2] of 247.44 µmol mol−1 and a δ13C of −20.45‰ using the lower calibration span (#1), and a total [CO2] of 247.43 µmol mol−1 and a δ13C of −20.45‰ using the higher calibration span (#2), a net difference of 0.01 µmol mol−1 and 0.00‰. We also determined the [CO2] and δ13C of the 142.86 µmol mol−1 WMO tank using gain and offset values calculated using the higher calibration span (#2). The result was a total [CO2] of 142.66 µmol mol−1 and a δ13C of −7.88‰, a net difference of 0.20 µmol mol−1 and 0.08‰ from SIL-certified values. Based on this assessment, we conclude our TDL has a linear response that extends beyond the lowest CO2 range we measured in this study.
The IRGA was calibrated the morning of each measurement day, and the reference and sample gas analysers of the IRGA were frequently matched to the same gas stream, while disconnected from the TDL inlet tubes. After reconnecting the TDL inlet tubes with the IRGA, the system was leak tested by gently blowing around the chamber, all connections and the pressure-equilibrating vent tube located on the sample line to the TDL. The TDL was also used to measure the reference and sample gas streams with an empty leaf chamber, and differences were lower than instrument precision (data not shown).
where ξ = ce/(ce − co) is the ratio of the reference CO2 concentration entering the chamber (ce) relative to the sample CO2 concentration outgoing from the chamber (co), and δe and δo are the δ13C of the reference and sample gas, respectively. All variables incorporated in Δobs and δ13Cresp (below) are derived from TDL measurements of [12CO2] and [13CO2], removing interinstrument variability. Mixing ratios of total [CO2] were calculated following Barbour et al. (2007a). Because the TDL measures the concentration of each isotopologue, δo and δe are calculated from the ratio of the molar abundance of each isotopologue and then presented in ratio to the Vienna Pee Dee belemnite (VPDB) standard, that is, δ = Rs/RVPDB − 1, where δ represents either δo or δe, and Rs and RVPDB represent the carbon isotope ratio of the sample and VPDB standard, respectively. We determined δ13Cresp following Barbour et al. (2007a):
where p equals (co − ce)/co. We estimated the δ13C of assimilated sugars (δ13Cs) based on Farquhar et al. (1989), where δ13Cs = (δe − Δobs)/(Δobs + 1). All other reported gas exchange values are calculated by the Li-6400 software following the methods of Farquhar, Caemmerer & Berry (1980), after correcting for leaf area. We determined the projected leaf area using a calibrated leaf area metre (Li-3100; Li-Cor Biosciences), and all gas exchange calculations are reported on a projected leaf area basis.
where ab, a, aw, bs and b are the fractionation factors associated with CO2 diffusion through the leaf boundary layer (2.9‰), stomata (4.4‰), water (0.7‰), fractionation attributed with CO2 entering solution (1.1‰) and the net fractionation attributed to phosphoenolpyruvate carboxylase and ribulose-1,5-bisphosphate carboxylase/oxygenase activity (estimated at 29‰; Roeske & O'Leary 1984), respectively. The variables pa, ps, pi and pc represent the partial pressure (Pa) of CO2 in the atmosphere surrounding the leaf, at the leaf surface, in the intercellular spaces and at the sites of carboxylation, respectively. The variables Γ*, Rd, k, f and e represent the CO2 compensation point (Pa) in the absence of day respiration, day respiration rate (µmol m−2 s−1), carboxylation efficiency (µmol m−2 s−1 Pa−1), and fractionations associated with photorespiration and day respiration (‰; see Table 1 for values), respectively. We calculated pa, ps and pi by incorporating mole fraction measurements of [CO2] with atmospheric pressure in Los Alamos (mean = 79 kPa), and estimated pc following Farquhar & Sharkey (1982):
Table 1. Parameters used in model simulations of observed discrimination using the comprehensive model (Δcomp) and the revised model (Δrevised). The fractionation factors associated with day respiration, e, and photorespiration, f, were assumed based on literature values while all the other terms are derived from our data
−11.5 to −1.6
−12.5 to −0.9
−10.5 to 1.2
where gi is internal conductance to CO2 (µmol m−2 s−1 Pa−1). We chose a moderate gi of 1.5 µmol m−2 s−1 Pa−1 based on the range of gi values observed over the study period. Prevailing theory suggests Γ* is highly conserved among C3 species, and previous work has demonstrated a strong temperature dependence of the CO2 photocompensation point (Jordan & Ogren 1984; Brooks & Farquhar 1985), on which we based our calculations of diurnal Γ*. Our Γ* calculations accounted for the reduced atmospheric pressure in Los Alamos, and we confirmed our estimates of Γ* with those calculated using the Sharkey et al. (2007) A/pi estimating utility (Table 1). Strictly, k, the carboxylation efficiency, is A/pc; we used the initial slope of A/pi response curves (n = 10) as a surrogate estimate and confirmed these slope-based results with calculations presented in Ku & Edwards (1977) and Wingate et al. (2007) (Table 1). Much work has demonstrated an inhibitory effect of light on respiration rate, even at an irradiance as low as 12 µmol m−2 s−1 (Atkin et al. 2000; Tcherkez et al. 2005, 2008). To facilitate estimation of Rd, we measured nocturnal respiration rate (PPFD = 0) on all 3 d for approximately 120 min after cessation of daytime measurements (see Results) and used these data to calculate an estimated Rd value for each day, where Rd = 0.5R (Tcherkez et al. 2005) and R equals steady-state respiration rate 30–120 min post-illumination (Table 1). We parameterized the decarboxylation component of Δcomp using constant f (8‰) (Rooney 1988; Tcherkez 2006) and e (−6‰) (Ghashghaie et al. 2003) values. Parameterizing e based on δ13Cresp (typically estimated at −6‰) may be problematic because of shifts in respiratory biochemistry under illuminated conditions (Tcherkez et al. 2008). We assessed the magnitude of uncertainty introduced at high and low A when varying e by comparing (Rd/A) × (pc/pa) multiplied by values of e = −6 and −1‰, and calculating the resulting variation in the Δef term (see Eqn 11).
We also ran model simulations following the recent revisions to the comprehensive model (Eqn 3) put forward by Wingate et al. (2007):
where e* represents apparent fractionation for day respiration expressing the difference between the isotopic composition of the respiratory substrate and photosynthetic assimilates at a given time (Table 1). We calculated an e* value for each three minute isotopic measurement using the following equation:
where δ13pa is the carbon isotope ratio of atmospheric air in the leaf chamber, and δ13Cmean equals the mean calculated from the δ13Cresp measurements for each measurement date (see Results). In Δrevised, we used a constant e, f, Rd, gi and k and a temperature-dependent Γ* (Table 1). Lastly, we modelled Δ for comparison to Δobs using the most simplified form of the Farquhar et al. (1982) model (Δsimple), which eliminates boundary layer, gi and decarboxylation contributions to CO2 flux and their associated fractionation factors:
where b = 27‰ (Gessler et al. 2008). All modelling was performed in Microsoft Excel XP Professional.
where ri is the internal resistance to CO2 transfer estimated as the slope of predicted 13C discrimination minus Δobs versus A/pa. In this application, predicted discrimination (Δi) was determined using Eqn 3 calculated with infinite gi, i.e. pi = pc. In this study, variation in A/pa was the result of natural variation in the leaf environment. We calculated slopes for each time period where new leaf material was enclosed in the leaf chamber, and tested each slope using a simple linear regression. All negative slopes were rejected because negative slopes result in negative gis estimates. All regression analyses were performed using JMP 5.0.1 (SAS Institute Inc., Cary, NC, USA). We used significant (P ≤ 0.10) slope values to estimate gis for each foliage measurement, and determined the viability of each gis estimate by comparing them to A across the entire measurement period. If the gis estimate was too low to facilitate observed A during any portion of the measurement period, we deemed that estimate to be erroneous. Finally, based on the theory developed by Evans et al. (1986) and Caemmerer & Evans (1991), we used the y-intercept of significant gis plots to estimate Δef.
where Δpred represents a simplified predictive model of leaf Δ:
and Δef is calculated as:
where all factors are the same as described in Δcomp (Eqn 3).
gi sensitivity analysis
We assessed the sensitivity of Δcomp to changes in gi by holding all parameters listed in Table 1 constant and by varying the gi value used to calculate pc over each day. We used gi values ranging from 0.5 to 2.5 µmol m−2 s−1 Pa−1, and applied each value uniformly across each measurement day.
We estimated the error in Δobs and δ13Cresp by implementing the parametric bootstrap (Davison & Hinkley 1997); we describe the procedure for Δobs, but δ13Cresp can be substituted in the description. For each measurement cycle, we used the sample mean and SEs of the concentrations of 12CO2 and 13CO2 for the high WS tank, low WS tank, reference gas and sample gas to define eight normal distributions. We drew eight random deviates of [12CO2] and [13CO2] from these distributions, calculated a bootstrap replicate of Δobs, and repeated this 10 000 times to provide a bootstrap sampling distribution of Δobs. This insured that the variance measured with each isotopologue was propagated into each calculation of ce, co, ξ, δe andδo and, therefore, into Δobs and δ13Cresp. The SE of the bootstrap replicates provides an estimate of the SE of Δobs. We observed that the bootstrap sampling distributions of Δobs were roughly normal, so the estimated SE characterizes the variation in Δobs. All bootstrap analyses were performed in R (R Core Development Team 2008) .
For both gis and gip, the gi estimate is a reciprocal transformation of a normally distributed random variable. While the SEs describe the normal distributions well, they are not easily interpretable for the skewed distributions associated with gis and gip. gis is the reciprocal of ri, estimated using the normally distributed regression slope (Table 2). For the slope-based gi, we calculated ri and ri ± 1 SE, and transformed these three values to the gi scale (Eqn 8) to generate gi and an estimate of its error. Similarly, for the point-based gi, we calculated the roughly normally distributed bootstrap mean Δobs ± 1 SE and transformed these to the gi scale (Eqn 9). For these data, 1 SE on the ri or Δobs scale is asymmetric on the gi scale with the upper SE being roughly twice the lower SE.
Table 2. Slope and intercept statistics from linear regressions used to calculate gis and estimate Δef. Cut-off values for the test of slope significance within each regression was P ≤ 0.10, but three marginal slopes are also represented (*). Most intercepts were not significantly different from zero, but significant intercepts (P ≤ 0.10) deviated substantially from zero
To assess model performance, we first used least squares regression analysis of predicted and observed values but found that the residual analysis of data in all months and models exhibited a non-random distribution. Additionally, both the slope and intercept terms were significantly different from one and zero, respectively, and substantially different from one another, making model comparisons difficult to evaluate. We then modified the computation of the residuals so that all models conformed to a slope of one and an intercept of zero (i.e. residuals = model prediction − observed data), and calculated the SD of the residuals. These SD values represented the square root of the sum of the variance and squared model bias, or the root mean square error (RMSE), for each month and model, and facilitated a direct comparison of the predictive performance between models within each month.
Juniper Δobs averaged (mean ± SE) 16.3 ± 0.2‰ in June, 17.2 ± 0.2‰ in July and 19.0 ± 0.5‰ in August (P ≤ 0.0002 between each). Leaf Δobs tended to be highest in the early morning in all three months, followed by midmorning variability and a decline through much of the afternoon (Fig. 1). The seasonal Δobs trend tracked the transition from low (June) to high (August) soil, leaf and atmospheric water content (Table 3, Fig. 2d–f). Similarly, the diurnal trend towards lower Δobs in the afternoon reflects the transition from relatively high morning leaf ψw to lower midday ψw (Table 3). On July and August measurement days, the variation in leaf Δobs reflects the stability of the light environment, with a relatively stable PPFD in July concurrent with a stable Δobs and a heterogeneous light environment in August resulting in fluctuating Δobs (Fig. 2). On 14 August, we lack reliable isotopic data after 1300 h because of low ambient light (PPFD < 100 µmol m−2 s−1), preventing A rates high enough to sustain reliable isotopic measurements. We found a weak but significant correlation between leaf vapour pressure deficit (VPD) and Δobs (r2 = 0.20, P < 0.0001; F = 110.22; Fig. 3), PPFD and Δobs (r2 = 0.20, P < 0.0001; F = 114.11), and A and Δobs (r2 = 0.11, P < 0.0001; F = 54.97; Fig. 3) using data pooled across all 3 d. Excluding the seven very high Δobs values in the early August morning, there was a significant relationship between stomatal conductance (gs) and Δobs (r2 = 0.03, P < 0.0001; F = 16.60; Fig. 3).
Table 3. Mean xylem water potential with SE on all three measurement days. Midday values from McDowell et al. (2008b)
Pre-dawn ψw (MPa)
Midday ψw (MPa)
The isotopic composition of nocturnal respiration was similar in June (mean = −22.6 ± 0.2‰) and July (mean = −22.7 ± 0.2‰; P = 0.70) (Fig. 4), while respiration rates were dissimilar (2.6 ± 0.04 and 4.8 ± 0.1 µmol m−2 s−1, respectively; P < 0.0001). In August, mean δ13Cresp was more depleted (mean = −23.5 ± 0.1‰) than values measured in June (P < 0.0001) and July (P < 0.0001), while respiration rate (mean = 3.7 ± 0.004 µmol m−2 s−1) was higher than that observed in June (P < 0.0001) and lower than that observed in July (P < 0.0001). These δ13Cresp values were enriched compared with estimates of the composition of recently assimilated sugars, which were −24.66 ± 0.20‰ in June, −25.19 ± 0.17‰ in July and −25.97 ± 0.30‰ in August. The step change in δ13Cresp observed approximately 50 min post-illumination in June and July was due to cessation of measurement on one group of foliage and the movement to new foliage.
Temporal variation in gi and Δef
We tested 32 slopes and found that 17 were significant across the 3 d. These produced 14 viable gis and Δef estimates based on comparisons to A, including two in June, six in July and six in August (Fig. 5; Table 2). We also found three slopes in the August morning, which failed our criteria for having a significant slope (P ≤ 0.1), but whose estimates of gis fit the observed trend and are included in Fig. 5 (Table 2). Other gis estimates failed to support observed A or displayed negative slope relationships between Δi−Δobs and A/pa, and were excluded from the analysis. Estimates of gip produced non-viable values when Δobs was larger than Δpred in bootstrap resamples, resulting in negative gip estimates. These 98 negative values, representing 22% of all gip estimates, were excluded from the analysis.
Internal conductance calculated from slope-based measurements ranged from 0.04 to 2.14 µmol m−2 s−1 Pa−1 (mean ± SE = 1.06 ± 0.17 µmol m−2 s−1 Pa−1) across the 3 d. The 14 August gis measurements were obtained from one leaf area across the morning and early afternoon, and demonstrated an increase in gis from 0.04 to 2.14 µmol m−2 s−1 Pa−1 (Fig. 5c). We observed a lower range of variability in July gis, with afternoon values ranging between 0.92 and 1.3 µmol m−2 s−1 Pa−1. We did not find a significant relationship between leaf temperature (Tl) and gis (r2 = 0.003, P = 0.87; F = 0.028). Estimates of gip ranged between 0.05 and 8.53 µmol m−2 s−1 Pa−1 (mean ± SE = 1.89 ± 0.07 µmol m−2 s−1 Pa−1) across the three measurement days (Fig. 5). Sensitivity analysis demonstrated a significant increase (P < 0.0001) in gip estimates when varying e = −6‰ and f = 8‰ (mean ± SE = 1.60 ± 0.04 µmol m−2 s−1 Pa−1) to e = −1‰ and f = 11‰ (3.31 ± 0.14 µmol m−2 s−1 Pa−1). There was a small but significant relationship between gip and Tl (r2 = 0.03, P = 0.0003; F = 13.168).
Δef also exhibited diurnal variation, ranging between −21.3 and +1.34‰. In August, we observed a low Δef value of −21.3‰ in the early morning, later morning values that were not significantly different from zero (P ≤ 0.10), and afternoon values near −2.5‰ (Table 2). The morning value in July was not significantly different from zero, whereas the afternoon Δef values were between −4.9 and −3.5‰. Our single significant Δef value in June was −10.56 ± 5.3‰. The non-zero values of Δef occur at early morning, midday or late afternoon, when fluxes are small and errors are likely to be greatest (Table 2).
Δobs and pi/pa
First-order linear relationships between Δobs and pi/pa were significant in June (r2 = 0.25, P < 0.0001; F = 58.31; Fig. 6a), July (r2 = 0.51, P < 0.0001; F = 182.61) and August (r2 = 0.72, P < 0.0001; F = 248.99); however, second-order polynomials described the relationships with greater predictive power in July (r2 = 0.64, P < 0.0001; F = 151.90) and August (r2 = 0.88, P < 0.0001; F = 334.27; Fig. 6b,c). The curvilinear relationship between Δobs and pi/pa was most pronounced in the pi/pa range between 0.75 and 0.85.
gi sensitivity analysis
Incorporation of variable gi into Δcomp over diurnal periods produced variation in predictions of Δcomp. Sensitivity analysis demonstrated using low gi (0.5 µmol m−2 s−1 Pa−1) in Δcomp resulted in a mean 6.9‰ underestimate of Δobs, while relatively high gi (2.5 µmol m−2 s−1 Pa−1) resulted in a 0.70‰ overestimate of Δobs (Table 4). Pairwise comparisons of the residuals (Δobs−Δcomp) resulting from Δcomp predictions incorporating a gi value of 0.5 µmol m−2 s−1 Pa−1 were significantly different from the residuals produced when using gi values of 1.0, 1.5, 2.0 and 2.5 µmol m−2 s−1 Pa−1 in Δcomp[P ≤ 0.05; Tukey's Honestly Significant Differences (HSD)] within and across all 3 d. Similarly, all other gi inputs into Δcomp (1.0, 1.5, 2.0 and 2.5 µmol m−2 s−1 Pa−1) produced significantly different residuals from one another within each day and across all 3 d (Table 4). The RMSE, a measure of the variance and squared bias associated with the residuals, largely followed the trend observed in the pairwise residual comparisons and was lower when residual differences were smaller; this demonstrates the importance of an accurate estimate of gi for model fit. Internal conductance values of 1.5 and 2.0 µmol m−2 s−1 Pa−1 produced the best predictions, as determined by the lowest pairwise residual differences and RMSE, when applied uniformly across each measurement day (Table 4).
Table 4. Results from a sensitivity analysis utilizing variable gi values within Δcomp and applied across each measurement day. Δobs − Δcomp represents the pairwise residual difference (‰) between observed discrimination (Δobs) and model predictions (Δcomp). Δcomp predictions using each of the gi values produced residuals significantly different from one another within each day and across days. As determined by the lowest root mean square error (RMSE; ‰) and pairwise residual difference, gi of 1.5 and 2.0 µmol m−2 s−1 Pa−1 performed best in predicting Δobs
n = 177
n = 176
n = 97
Model predictions: Δcomp, Δrevised and Δsimple
Model performance varied across the three measurement days (Fig. 7). Assessing the error between model predictions and Δobs in each month showed that Δsimple had the lowest RMSE, 2.11‰, in June, Δcomp had the lowest error in July (RMSE = 1.50‰), and Δrevised exhibited the lowest error in August (RMSE = 3.15‰; Table 5). Substituting b = 25‰ into Δsimple reduced model prediction bias (mean = 0.31 ± 0.12‰) but resulted in higher RMSE (mean = 2.65‰ versus 2.42‰ for b = 27‰) on all 3 d compared with using b = 27‰. The estimated model prediction bias between Δcomp, Δrevised and Δsimple and observed discrimination across all three dates was (mean ± SE) −0.62 ± 0.18‰, −0.28 ± 0.19‰ and 1.63 ± 0.18‰, respectively. However, error assessment revealed that the apparent close simulations suggested by the small model prediction bias between modelled and observed values masked substantial variance in all models' predictions of Δobs (Table 5). At high A, defined here as >4.0 µmol m−2 s−1, uncertainty introduced into Δef by utilizing e = −6‰ versus −1‰ was equal to 2.21 ± 0.01‰, while at low A, defined here as <2.0 µmol m−2 s−1, the same uncertainty increased to 9.40 ± 1.51‰ (Table 6).
Table 5. Comparison of model performance in predicting Δobs. Means represent the difference between model predictions and Δobs (bias) and the root mean square error (RMSE). Δsimple consistently overestimated Δobs but showed a lower error in predicting Δobs in June compared with Δcomp and Δrevised. Δcomp exhibited the lowest error in July, while Δrevised exhibited a lower error and mean difference between predicted and observed values in August compared with Δsimple and Δcomp
n = 177
n = 176
n = 97
Table 6. Results from a sensitivity analysis assessing the variation in Δef, the decarboxylation term in Δcomp, when parameterized with e = −6‰ and e = −1‰. The uncertainty introduced into the decarboxylation term at low to high net photosynthetic rate (A) when varying e from −6 to −1‰ is represented in Δef uncertainty (‰). This demonstrates that Δef is very sensitive to variation in e at low A; in this study, <4% of all measurements were at A < 2.0 µmol m−2 s−1
A (µmol m−2 s−1)
Δef uncertainty (‰)
The objectives of this study were to (1) examine the temporal variation in Δ, δ13Cresp, gi and Δef under ambient field conditions; (2) test the hypothesis that gi varies across the day; (3) test the hypothesis that Δ varies linearly in response to shifts in pi/pa under field conditions; (4) test the influence of gi in a comprehensive leaf model of Δ; and (5) test the predictive capabilities of three models: the comprehensive Farquhar et al. (1982) model of Δ (Δcomp), a recently suggested amendment to Δcomp (Δrevised; Wingate et al. 2007) and the simplified form of the comprehensive model (Δsimple). We observed a large range of variation in Δ, gi and Δef over diurnal time periods and across the season. Seasonally, δ13Cresp decreased as water availability increased. We found that gi varied across the day in August and that gi exerted substantial influence on Δ predictions. We found Δobs varied in a linear fashion in response to pi/pa in June, but second-order expressions better described the relationship in July and August. Finally, we found all models reasonably predicted Δobs, but Δsimple best predicted Δobs in June, Δcomp best predicted Δobs in July, and Δrevised best predicted Δobs in August.
Diurnal Δobs and nocturnal δ13Cresp
Diurnal Δobs in our juniper woodland varied between 12.0 and 27.4‰, which was similar in trend and magnitude to Δ observed in a tropical forest (Harwood et al. 1998) and in a mesic Picea stand (Wingate et al. 2007) (Fig. 1). Variation in Δobs was generally related to environmental drivers such as PPFD and VPD (Figs 1–3). An inverse relationship between VPD and Δobs was apparent diurnally and seasonally, although low leaf ψw and high air temperature likely contributed to low discrimination in June compared with July and August. In August, VPD was relatively low and cloudy conditions caused large variation in Δobs. Cumulatively, these sensitivities to VPD and PPFD were similar to those seen in modelled canopy Δ (Baldocchi & Bowling 2003; Chen & Chen 2007). We also observed several high, but transient, discrimination values in all 3 months including midday values of 31.4‰ in June and 36.9‰ in July, and observations ranging from 29.7 to 44.9‰ in the early morning in August. These Δobs values were associated with greater uncertainty, but were similar to values observed in Piper and Picea (Harwood et al. 1998; Wingate et al. 2007).
Nocturnal δ13Cresp for the juniper trees in our study ranged from ∼ −24 to −21‰, and was moderately enriched compared with most observations in the literature (Bowling et al. 2002; Hymus et al. 2005; Prater, Mortazavi & Chanton 2005). δ13Cresp values were similar in June and July, and were more enriched in 13C compared with the values in August (Fig. 4). The consistent 2–3‰ enrichment of δ13Cresp compared to estimates of recently assimilated carbohydrate is consistent with previous reports (Duranceau et al. 1999; Ghashghaie et al. 2001) and may reflect respiratory fractionation, possibly combined with diverse respiratory substrate utilization (Tcherkez et al. 2003). This δ13Cresp pattern is consistent with the temporal transition period from drought in June through the onset of summer monsoon in July to the strong monsoon in August.
Temporal variation in gi and Δef
We observed a diurnal increase in gi occurring in one leaf area across the August morning and early afternoon, and a range of variation in gi across the 3 months (Fig. 5). The physiological drivers of this variation in gi are unknown, but likely involved changes in protein activity facilitating the transfer of CO2 across cell or chloroplast membranes (Flexas et al. 2006; Hanba et al. 2006; Uehlein et al. 2008). Previous work has demonstrated variability in gi in response to environmental variables such as temperature (Bernacchi et al. 2002; Warren & Dreyer 2006; Yamori et al. 2006) and water availability (Warren et al. 2004; Grassi & Magnani 2005; Galmés, Medrano & Flexas 2007; Diaz-Espejo et al. 2007), both of which fluctuate in a field setting. We did not find a significant correlation between Tl and gis, but we did find a significant relationship between Tl and gip. It is possible that variable irradiance over each measurement period may have confounded any temperature effect on gis, but the higher temporal frequency of gip was closer to the frequency Tl was changing diurnally. Juniper displays anisohydric leaf hydraulic behaviour, and concurrent ψw measurements (Table 3) demonstrated a seasonal increase and diurnal decrease in xylem ψw. The seasonal ψw pattern paralleled our seasonal gi measurements, suggesting a linkage between leaf water status and the gi patterns we observed, but are confounded by the increase in both gis and gip in the August morning when ψw was decreasing. Notably, there was a distinct decrease in gis in the upward morning trend that coincides with extended cloud cover (mean PPFD = 266 ± 46 µmol m−2 s−1). We speculate that the large and prolonged drop in incident light played a regulatory role in the lower gi, similar to observations of other environmental regulators of gi in controlled studies (Delfine et al. 1999; Bernacchi et al. 2002; Flexas et al. 2007). The July data exhibit modest variation in diurnal gi, but may reflect natural variation among branches. Given that our measurements were collected under ambient environmental conditions, an accurate assessment of the factors driving the variation in gi we observed is not possible and should be addressed in controlled studies.
The variation in gis is potentially problematic for the slope-based method because it assumes that gi is constant over the period the slope data are collected. While rapid variation in gi has been demonstrated in response to [CO2] (Flexas et al. 2007), the rate and magnitude of diurnal shifts in gi under field conditions have not been previously reported. Our 30–45 min gis measurement periods may have spanned too long and allowed time for gi to change in response to the environment. However, aside from periods where Δobs was highly variable, such as the July midday period, gip values were generally stable around each gis value and show that variation was low enough to provide valid gis estimates. Slope-based estimates of gi tended to be lower than gip in June and July, but both trended together in August (Fig. 5). gip is sensitive to the parameterization of e and f, and errors in estimating these values may have resulted in over- or underestimation of g.
Most of our gi estimates agree with values reported in other woody species (Lloyd et al. 1992; De Lucia, Whitehead & Clearwater 2003; Warren et al. 2003; Ethier et al. 2006), but we also found low gis estimates in the early morning and relatively high gip estimates when Δobs was highly variable. We found a low gis estimate (0.03 µmol m−2 s−1 Pa−1) in the August early morning transition period from respiration to net A, where net CO2 drawdown was between 6 and 10 µmol mol−1, uncertainty in Δobs was higher, and measurements may have been more strongly influenced by the isotopic signature of CO2 evolved during concurrent day respiratory processes. Although low, model simulations demonstrated that the 0.03 µmol m−2 s−1 Pa−1 conductance estimate was high enough to allow observed A across the measurement period. Estimates from gip during this period show consistently negative estimates of gi (data not shown). High and variable gip estimates ranged between 4 and 8 µmol m−2 s−1 Pa−1 during the midday period in July, driven by higher uncertainty in Δobs over this period.
Our measurements of Δef suggest that fractionations attributed to decarboxylation activity may not be negligible at dawn and in the afternoon when rates of either respiration or photorespiration may be high (Table 2). Our early morning August measurement occurred during a time of low A/pa and generated a very negative Δef value. If respiration had not fully deactivated to its daytime rate, then it may have had an unusually large impact during that time period (Gillon & Griffiths 1997). By midmorning in July and August, A and gs had reached a plateau, and Δef was not significantly different from zero. However, in the June and July afternoons, high temperature and PPFD created conditions conducive to higher photorespiration rates that may have contributed to greater variation in the afternoon Δef values. Further, compared with other C3 species, juniper exhibits high R, from which we estimated Rd, and thus the respiratory component of Δef would have a larger impact on net Δ than would be expected for other species. Carefully controlled studies partitioning different components of the net flux will be necessary to elucidate the contribution of each component.
Δobs and pi/pa
We observed significant first-order linear relationships between Δ and pi/pa in all months, but found that second-order models better described the curvilinear relationship between Δ and pi/pa in July and August (Fig. 6). We propose that the curvilinear relationship is related to the increasing dominance of respiration and associated isotopic signatures on leaf-exchanged CO2at high pi/pa values. Previous work and theory have demonstrated a linear relationship between Δ and pi/pa in C3 plants (Farquhar et al. 1982b, 1989; Evans et al. 1986; Brugnoli et al. 1988), but unlike our study, these data were collected in controlled settings under steady-state conditions. In both July and August, the curvilinear trend between Δ and pi/pa was driven by high Δ values. These high Δ values correspond with conditions conducive to high respiratory and photorespiratory flux, notably the early morning and midday periods, and may reflect the isotopic signature of a highly enriched substrate.
gi sensitivity analysis
Incorporating variable internal CO2 conductance into Δcomp demonstrated that gi exerted substantial influence on predictions of diurnal discrimination. Average-observed gi was near 1.5 µmol m−2 s−1 Pa−1, and our sensitivity analysis showed that relatively low (0.5 µmol m−2 s−1 Pa−1) and high (2.5 µmol m−2 s−1 Pa−1) values resulted in large deviations between model predictions and Δobs (Table 4). However, we have shown that gi can vary in a leaf over several hours, and it is likely that incorporating this diurnal variability into leaf and ecosystem models would improve discrimination predictions (McDowell et al. 2008a). Future studies should focus on assessing the diurnal variability in gi independently and on testing whether variable diurnal gi significantly improves the accuracy and precision of predictions of Δ in leaf models.
Model predictions: Δcomp, Δrevised and Δsimple
Our study supports the use of the more comprehensive models, Δcomp and Δrevised, that incorporate fractionations associated with the diffusion pathway and decarboxylation activity, to describe leaf Δ in our semi-arid system. The limitations of these models are that they require assumptions of the true value of fractionation during carboxylation and decarboxylation, in addition to an accurate estimate of gi. Our sensitivity analysis showed that variation in e at low A resulted in ∼9‰ variation in Δef, emphasizing the importance of e in plants, such as juniper, that exhibit relatively high R compared with A. Our estimate of e was based on the dark respiration fractionation, and we may have over- or underestimated the true value of e or Rd and introduced model error. However, we have shown that both models produced similar errors in their predictions of Δ.
The importance of decarboxylation activity in juniper Δ is reflected both in the e* values we calculated and the Δef estimates obtained from gi plots. We calculated e* values ranging from −12.5 to +1.2‰, values that suggest the isotopic disequilibria between recent photosynthate and the respiratory substrate being utilized was, at times, substantial. Further, our Δef estimates were mostly between −6.9 and 0‰, whereas previous observations were close to 0‰ (Evans et al. 1986). It is also possible that other factors, such as stomatal patchiness, may not be fully captured in our estimates of pi, which could alter the pi/pa ratio important to all of the Δ models (Farquhar 1989).
Despite lacking decarboxylation and gi components, Δsimple outperformed the more comprehensive models in June. Further, Δsimple exhibited modest error in predicting Δobs compared with Δcomp and Δrevised in July and August, but consistently overestimated Δobs, predicting Δ values whose mean difference were >1.0‰ above Δobs in all 3 months. This may represent a larger systematic bias than that exists in the other models, although utilizing a lower b value reduced model bias while moderately increasing error. However, all of the models exhibited non-trivial RMSE, ranging from 1.5 to 3.2‰, suggesting that a significant amount of variability remains to be captured. Future field studies should aim to independently estimate the variability in diurnal Δef and gi to ascertain their impacts on diurnal leaf isotopic exchange. Similarly, future controlled studies should partition the net flux to assess gi and Δef, as well as the regulatory influence of environmental variables, such as temperature and PPFD, on these components of carbon discrimination.
Our study demonstrates that the diurnal variation in Δ in our semi-arid conifer ecosystem was of similar trend and magnitude to that observed in ecosystems as diverse as tropical forest and mesic conifer forest. Additionally, we demonstrated that Δ varies rapidly in response to shifts in environmental conditions, and that the comprehensive Farquhar et al. (1982) model and its descendents are capable of capturing a wide range of diurnal variation in leaf Δ. Our observations are consistent with previous results showing low Δ during conditions of low soil water availability and elevated VPD and PPFD, and higher Δ when soil water was more abundant, PPFD was variable, and VPD was low. We observed a linear relationship between Δ and pi/pa in June, but found a strong curvilinear relationship in July and August. Future studies might be strengthened by testing this relationship in other species over a wide range of pi/pa and environmental conditions. Our findings support the inclusion of gi and decarboxylation activity to attain the most accurate and precise predictions of Δ from leaf models, and evolving technologies, such as TDL, make these improvements more easily achievable. Lastly, the magnitude of diurnal variation in gi of other C3 species needs to be quantified, as do the environmental and physiological drivers of this variation, so that gi can be more accurately parameterized in future ecosystem process models.
We thank H. Powers, K. Brown and C. Meyer for extensive technical support, and the Institute of Geophysics and Planetary Physics at Los Alamos National Laboratory (project 95566-001-05), the National Science Foundation (IOS-0719118), UNM PIBBS and the UNM Biology Department Lynn A. Hertel Graduate Research Award for funding. We also thank Professor Graham Farquhar and two anonymous reviewers for their comments that improved the paper.