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 CO_{2} and its isotopologues ^{13}C^{16}O_{2} and ^{12}C^{16}O_{2} 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 CO_{2} 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 CO_{2} isotopologues ^{13}C^{16}O^{16}O and ^{12}C^{16}O^{16}O 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 *µ*mol s^{−1} to maintain a sufficient CO_{2} drawdown and control chamber humidity. We attempted to maintain CO_{2} drawdown ≥40 *µ*mol CO_{2} 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 (*δ*^{13}C_{resp}) was measured immediately following daylight measurements and beginning when ambient photosynthetic photon flux density (PPFD) fell below 30 *µ*mol photons m^{−2} s^{−1} and foliage exhibited net CO_{2} 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 CO_{2} concentration (*A*/*p*_{i}). 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 (*ψ*_{w}) 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 *µ*mol CO_{2} mol^{−1} air, *δ*^{13}C = −16.16‰ and 350.34 *µ*mol CO_{2} mol^{−1} air, *δ*^{13}C = −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 ^{12}CO_{2}:^{13}CO_{2} in the WS tanks used in the June campaign were 354.04 ± 0.27:3.82 ± 0.003 *µ*mol CO_{2} mol^{−1} air (mean ± standard error; *n* = 11 inter-tank calibrations) and 563.85 ± 0.27:6.09 ± 0.003 *µ*mol CO_{2} mol^{−1} air (*n* = 11). Molar mixing ratios of ^{12}CO_{2}:^{13}CO_{2} in the WS tanks used in the July and August campaigns were 340.46 ± 0.29:3.67 ± 0.003 *µ*mol CO_{2} mol^{−1} air (*n* = 10) and 518.71 ± 0.08:5.60 ± 0.001 *µ*mol CO_{2} mol^{−1} air (*n* = 6). The WMO-certified tanks were filled and *δ*^{13}C 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 *δ*^{13}C 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 ^{12}CO_{2} and ^{13}CO_{2} in each WS tank should span the measurement range. During the three measurement days, our measurements occasionally exceeded the lower end of the total [CO_{2}] in our WS tanks (maximum deviation: 45.7 *µ*mol mol^{−1}). To test that the calibration was valid below the lower tank, we used a WMO traceable standard tank (total [CO_{2}] = 142.86 *µ*mol mol^{−1}, *δ*^{13}C = −7.96‰) and an additional unknown tank that had a target total [CO_{2}] of 250 *µ*mol mol^{−1}. We measured these two tanks and two WS tanks (344.88 *µ*mol mol^{−1}, −8.16‰ and 548.16 *µ*mol mol^{−1}, −16.42‰) in series. We calculated the total [CO_{2}] 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 *µ*mol mol^{−1} tank and the 344.86 *µ*mol mol^{−1} tank and (2) using the span between the 344.86 *µ*mol mol^{−1} tank and the 548.16 *µ*mol mol^{−1} tank measurements. The unknown tank was calculated to have a total [CO_{2}] of 247.44 *µ*mol mol^{−1} and a *δ*^{13}C of −20.45‰ using the lower calibration span (#1), and a total [CO_{2}] of 247.43 *µ*mol mol^{−1} and a *δ*^{13}C of −20.45‰ using the higher calibration span (#2), a net difference of 0.01 *µ*mol mol^{−1} and 0.00‰. We also determined the [CO_{2}] and *δ*^{13}C of the 142.86 *µ*mol mol^{−1} WMO tank using gain and offset values calculated using the higher calibration span (#2). The result was a total [CO_{2}] of 142.66 *µ*mol mol^{−1} and a *δ*^{13}C of −7.88‰, a net difference of 0.20 *µ*mol 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 CO_{2} 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).

#### Δ and *δ*^{13}C_{resp} calculations

- (1)

where *ξ* = *c*_{e}/(*c*_{e} − *c*_{o}) is the ratio of the reference CO_{2} concentration entering the chamber (*c*_{e}) relative to the sample CO_{2} concentration outgoing from the chamber (*c*_{o}), and *δ*_{e} and *δ*_{o} are the *δ*^{13}C of the reference and sample gas, respectively. All variables incorporated in Δ_{obs} and *δ*^{13}C_{resp} (below) are derived from TDL measurements of [^{12}CO_{2}] and [^{13}CO_{2}], removing interinstrument variability. Mixing ratios of total [CO_{2}] were calculated following Barbour *et al.* (2007a). Because the TDL measures the concentration of each isotopologue, *δ*_{o} and *δ*_{e} 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* = *R*_{s}/*R*_{VPDB} − 1, where *δ* represents either *δ*_{o} or *δ*_{e}, and *R*_{s} and *R*_{VPDB} represent the carbon isotope ratio of the sample and VPDB standard, respectively. We determined *δ*^{13}C_{resp} following Barbour *et al.* (2007a):

- (2)

where *p* equals (*c*_{o} − *c*_{e})/*c*_{o}. We estimated the *δ*^{13}C of assimilated sugars (*δ*^{13}C_{s}) based on Farquhar *et al.* (1989), where *δ*^{13}C_{s} = (*δ*_{e} − Δ_{obs})/(Δ_{obs} + 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.

#### Model parameterization

- (3)

where *a*_{b}, *a*, *a*_{w}, *b*_{s} and *b* are the fractionation factors associated with CO_{2} diffusion through the leaf boundary layer (2.9‰), stomata (4.4‰), water (0.7‰), fractionation attributed with CO_{2} 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 *p*_{a}, *p*_{s}, *p*_{i} and *p*_{c} represent the partial pressure (Pa) of CO_{2} in the atmosphere surrounding the leaf, at the leaf surface, in the intercellular spaces and at the sites of carboxylation, respectively. The variables *Γ**, *R*_{d}, *k*, *f* and *e* represent the CO_{2} compensation point (Pa) in the absence of day respiration, day respiration rate (*µ*mol m^{−2} s^{−1}), carboxylation efficiency (*µ*mol m^{−2} s^{−1} Pa^{−1}), and fractionations associated with photorespiration and day respiration (‰; see Table 1 for values), respectively. We calculated *p*_{a}, *p*_{s} and *p*_{i} by incorporating mole fraction measurements of [CO_{2}] with atmospheric pressure in Los Alamos (mean = 79 kPa), and estimated *p*_{c} following Farquhar & Sharkey (1982):

Table 1. Parameters used in model simulations of observed discrimination using the comprehensive model (Δ_{comp}) and the revised model (Δ_{revised}). 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 Day | Parameters | Δ_{revised} only |
---|

*k* | *R*_{d} | *Γ** | *e* | *f* | *g*_{i} | *e** |
---|

12 June | 0.38 | 1.23 | 2.86–5.23 | −6 | 8 | 1.5 | −11.5 to −1.6 |

11 July | 0.40 | 2.2 | 3.17–5.17 | −6 | 8 | 1.5 | −12.5 to −0.9 |

14 August | 0.40 | 1.83 | 2.43–4.29 | −6 | 8 | 1.5 | −10.5 to 1.2 |

- (4)

where *g*_{i} is internal conductance to CO_{2} (*µ*mol m^{−2} s^{−1} Pa^{−1}). We chose a moderate *g*_{i} of 1.5 *µ*mol m^{−2} s^{−1} Pa^{−1} based on the range of *g*_{i} values observed over the study period. Prevailing theory suggests *Γ** is highly conserved among C_{3} species, and previous work has demonstrated a strong temperature dependence of the CO_{2} 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*/*p*_{i} estimating utility (Table 1). Strictly, *k*, the carboxylation efficiency, is *A*/*p*_{c}; we used the initial slope of *A*/*p*_{i} 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 *µ*mol m^{−2} s^{−1} (Atkin *et al.* 2000; Tcherkez *et al.* 2005, 2008). To facilitate estimation of *R*_{d}, 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 *R*_{d} value for each day, where *R*_{d} = 0.5*R* (Tcherkez *et al.* 2005) and *R* equals steady-state respiration rate 30–120 min post-illumination (Table 1). We parameterized the decarboxylation component of Δ_{comp} using constant *f* (8‰) (Rooney 1988; Tcherkez 2006) and *e* (−6‰) (Ghashghaie *et al.* 2003) values. Parameterizing *e* based on *δ*^{13}C_{resp} (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 (*R*_{d}/*A*) × (*p*_{c}/*p*_{a}) multiplied by values of *e* = −6 and −1‰, and calculating the resulting variation in the Δ_{ef} 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):

- (5)

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:

- (6)

where *δ*^{13}*p*_{a} is the carbon isotope ratio of atmospheric air in the leaf chamber, and *δ*^{13}C_{mean} equals the mean calculated from the *δ*^{13}C_{resp} measurements for each measurement date (see Results). In Δ_{revised}, we used a constant *e*, *f*, *R*_{d}, *g*_{i} and *k* and a temperature-dependent *Γ** (Table 1). Lastly, we modelled Δ for comparison to Δ_{obs} using the most simplified form of the Farquhar *et al.* (1982) model (Δ_{simple}), which eliminates boundary layer, *g*_{i} and decarboxylation contributions to CO_{2} flux and their associated fractionation factors:

- (7)

where *b* = 27‰ (Gessler *et al.* 2008). All modelling was performed in Microsoft Excel XP Professional.

#### Estimation of *g*_{i} and Δ_{ef}

- (8)

where *r*_{i} is the internal resistance to CO_{2} transfer estimated as the slope of predicted ^{13}C discrimination minus Δ_{obs} versus *A*/*p*_{a}. In this application, predicted discrimination (Δ_{i}) was determined using Eqn 3 calculated with infinite *g*_{i}, i.e. *p*_{i} = *p*_{c}. In this study, variation in *A*/*p*_{a} 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 *g*_{is} 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 *g*_{is} for each foliage measurement, and determined the viability of each *g*_{is} estimate by comparing them to *A* across the entire measurement period. If the *g*_{is} 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 *g*_{is} plots to estimate Δ_{ef}.

- (9)

where Δ_{pred} represents a simplified predictive model of leaf Δ:

- (10)

and Δ_{ef} is calculated as:

- (11)

where all factors are the same as described in Δ_{comp} (Eqn 3).

#### Statistical analysis

We estimated the error in Δ_{obs} and *δ*^{13}C_{resp} by implementing the parametric bootstrap (Davison & Hinkley 1997); we describe the procedure for Δ_{obs}, but *δ*^{13}C_{resp} can be substituted in the description. For each measurement cycle, we used the sample mean and SEs of the concentrations of ^{12}CO_{2} and ^{13}CO_{2} for the high WS tank, low WS tank, reference gas and sample gas to define eight normal distributions. We drew eight random deviates of [^{12}CO_{2}] and [^{13}CO_{2}] from these distributions, calculated a bootstrap replicate of Δ_{obs}, and repeated this 10 000 times to provide a bootstrap sampling distribution of Δ_{obs}. This insured that the variance measured with each isotopologue was propagated into each calculation of *c*_{e}, *c*_{o}, *ξ*, *δ*_{e} and*δ*_{o} and, therefore, into Δ_{obs} and *δ*^{13}C_{resp}. The SE of the bootstrap replicates provides an estimate of the SE of Δ_{obs}. We observed that the bootstrap sampling distributions of Δ_{obs} were roughly normal, so the estimated SE characterizes the variation in Δ_{obs}. All bootstrap analyses were performed in R (R Core Development Team 2008) .

For both *g*_{is} and *g*_{ip}, the *g*_{i} 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 *g*_{is} and *g*_{ip}. *g*_{is} is the reciprocal of *r*_{i}, estimated using the normally distributed regression slope (Table 2). For the slope-based *g*_{i}, we calculated *r*_{i} and *r*_{i} ± 1 SE, and transformed these three values to the *g*_{i} scale (Eqn 8) to generate *g*_{i} and an estimate of its error. Similarly, for the point-based *g*_{i}, we calculated the roughly normally distributed bootstrap mean Δ_{obs} ± 1 SE and transformed these to the *g*_{i} scale (Eqn 9). For these data, 1 SE on the *r*_{i} or Δ_{obs} scale is asymmetric on the *g*_{i} scale with the upper SE being roughly twice the lower SE.

Table 2. Slope and intercept statistics from linear regressions used to calculate *g*_{is} and estimate Δ_{ef}. 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 Campaign | Time (h) | Slope | SE | *P* | Δ_{ef} | SE | *P* | *r*^{2} |
---|

12 June | 0700 | 22.05 | 11.13 | 0.06 | −2.19 | 1.74 | 0.22 | 0.18 |

1300 | 108.63 | 46.77 | 0.05 | −10.56 | 5.35 | 0.08 | 0.40 |

11 July | 0900 | 54.81 | 22.07 | 0.05 | −12.03 | 6.4 | 0.11 | 0.51 |

1200 | 20.4 | 10.49 | 0.09 | −3.83 | 2.29 | 0.14 | 0.35 |

1300 | 27.58 | 10.55 | 0.03 | −3.58 | 2.13 | 0.14 | 0.49 |

1400 | 27.32 | 7.72 | 0.02 | −4.91 | 2.03 | 0.06 | 0.71 |

1500 | 21.44 | 7.65 | 0.01 | −3.53 | 1.79 | 0.07 | 0.34 |

1600 | 29.31 | 12.35 | 0.05 | −3.12 | 2.54 | 0.25 | 0.41 |

14 August | 0600 | 757.31 | 312.02 | 0.07 | −21.31 | 5.87 | 0.02 | 0.60 |

0700 | 87.24 | 23.82 | 0.008 | −1.28 | 1.52 | 0.42 | 0.66 |

0800* | 22.81 | 15.53 | 0.18 | −0.41 | 2.94 | 0.89 | 0.21 |

0900 | 20.21 | 4.39 | 0.0002 | 0.15 | 0.63 | 0.8 | 0.54 |

1000* | 15.23 | 8.47 | 0.11 | 1.39 | 1.52 | 0.39 | 0.29 |

1100 | 43.04 | 7.68 | 0.0005 | −3.33 | 0.89 | 0.006 | 0.80 |

1200* | 13.17 | 8.86 | 0.18 | −2.11 | 2.77 | 0.47 | 0.22 |

1300 | 12.69 | 3.83 | 0.01 | −1.54 | 1.19 | 0.23 | 0.58 |

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.