• discrimination;
  • isotopic disequilibrium;
  • Keeling plot;
  • partition;
  • photosynthesis.


  1. Top of page
  9. Appendices

Ecosystem-scale estimation of photosynthesis and respiration using micrometeorological techniques remains an important, yet difficult, challenge. In this study, we combined micrometeorological and stable isotope methods to partition net ecosystem CO2 exchange (FN) into photosynthesis (FA) and respiration (FR) in a corn–soybean rotation ecosystem during the summer 2003 corn phase. Mixing ratios of 12CO2 and 13CO2 were measured continuously using tunable diode laser (TDL) absorption spectroscopy. The dynamics of the isotope ratio of ecosystem respiration (δR), net ecosystem CO2 exchange (δN) and photosynthetic discrimination at the canopy scale (Δcanopy) were examined. During the period of full canopy closure, FN was partitioned into photosynthesis and respiration using both the isotopic approach and the conventional night-time-derived regression methodology. Results showed that δR had significant seasonal variation (−32 to −11‰) corresponding closely with canopy phenology. Daytime δN typically varied from −12 to −4‰, while Δcanopy remained relatively constant in the vicinity of 3‰. Compared with the regression approach, the isotopic flux partitioning showed more short-term variations and was considerably more symmetric about FN. In this experiment, the isotopic partitioning resulted in larger uncertainties, most of which were caused by the uncertainties in δN and the daytime estimate of δR. By sufficiently reducing these uncertainties, the tunable diode laser (TDL)–micrometeorological technique should yield a better understanding of the processes controlling photosynthesis, respiration and ecosystem-scale discrimination.


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  9. Appendices

Studies of stable isotope variation and exchange between ecosystems and the atmosphere can provide new insight into biological and physical controls on carbon cycling. Stable isotope analyses have been used to identify global carbon sources and sinks (Ciais et al. 1995; Lloyd, Krujit & Hollinger 1996; Fung et al. 1997; Battle et al. 2000), to partition ecosystem CO2 respiration (Flanagan & Ehleringer 1997; Rochette, Flanagan & Gregorich 1999), and particularly to partition the net ecosystem exchange of CO2 (FN) into photosynthesis (FA) and respiration (FR) (Yakir & Wang 1996; Hanson et al. 2000; Bowling, Tans & Monson 2001; Lai et al. 2003; Ogée et al. 2003). At present, FN is measured globally as part of the global FLUXNET network with the eddy covariance (EC) technique. However, measuring FA and FR directly remains an important and difficult challenge. Traditionally, FR is estimated using night-time-derived temperature regression models (Ruimy, Jarvis & Baldocchi 1995; Goulden et al. 1997), and FA is estimated using daytime light-response analyses (Falge et al. 2002; Griffis et al. 2003). However, these approaches may not adequately account for the physiological controls on respiration that are likely to differ between day and night (Brooks & Farquhar 1985; Janssens et al. 2001). Automated chambers have been used to quantify half-hourly values of component respiration and have been scaled up to the ecosystem (Drewitt et al. 2002; Griffis et al. 2004a), but the results have substantial uncertainty because of the relatively large spatial variation and limited number of chambers deployed. The chamber scaling also requires temperature-dependent algorithms. Single-layer and multilayer canopy models (Baldocchi & Harley 1995; Wang & Leuning 1998) have also been used in estimating FA. These physiological models usually require detailed canopy structure information and assumptions regarding scales that we ultimately want to test with the best available ecosystem-scale data. The parameterization of these models might be very specific to certain types of ecosystems, which further limits their universal application.

The stable isotope technique provides an independent methodology for short-term FN partitioning. Applying the mass balance principle, Yakir & Wang (1996) have partitioned FN using measurements of CO2 concentration and the isotope ratios of plant, soil and atmosphere over an agricultural ecosystem. However, their method is only applicable over relatively long timescales because the isotope ratios of plants and bulk soil organic matter represent integrative values and therefore do not explicitly account for the short-term dynamics of FA or FR. Through the combination of isotopic and micrometeorological techniques, Bowling et al. (2001) improved upon the methodology of Yakir & Wang (1996) by introducing short-term (i.e. half-hourly) canopy scale photosynthetic discrimination (Δcanopy) and by quantifying the isoflux [isoflux = ρinline image, where ρ is molar air density, w is vertical wind speed, Ca is CO2 mixing ratio, δa is the isotope ratio of ambient air, primes denote fluctuations from the mean and the overbar denotes time averaging], which is an isotopic approximation of the vertical flux of 13CO2. This methodology has also been applied to the partitioning of the FN of a C4-dominated grassland (Lai et al. 2003) and a temperate coniferous forest (Ogée et al. 2003).

In the isotopic flux partitioning, the isotope ratio of ecosystem respiration (δR) and the isoflux (or approximately, δN·FN, where δN is the isotope ratio of FN) are the two critical parameters that need to be determined. Traditionally, δR has been estimated using the Keeling plot method, which is based on the linear relationship between the isotope ratio and the reciprocal of the CO2 mixing ratio (Keeling 1958). However, the Keeling plot method is subject to a number of uncertainties. These include advection, variation in the isotopic composition of the background atmosphere and the extrapolation of CO2 mixing ratio to a value well beyond the usually narrow range of observation (Ogée et al. 2003; Pataki et al. 2003; Griffis et al. 2004b). Bowling et al. (2001) have estimated the isoflux using a Keeling-type function that has been tested over various timescales. However, this function might have considerable uncertainty when the CO2 range is narrow, which typically occurs during the daytime (Ogée et al. 2004). δN has been estimated as the slope of the regression between (δaCa − δbgCbg) and (Ca − Cbg), where Cbg and δbg are the assumed CO2 mixing ratio and the isotope ratio of the background atmosphere, respectively (Lai et al. 2004; Ogée et al. 2004). This approach is sensitive to the values chosen for Cbg and δbg and might not be appropriate for field-scale studies because of boundary layer dynamics.

The above partitioning studies relied on flask sampling and mass spectrometry laboratory analyses, limiting their temporal resolution. With the recent development of tunable diode laser (TDL) spectroscopy, continuous observation of stable isotopomer mixing ratios (12CO2 and 13CO2) at high temporal resolution is now possible (Bowling et al. 2003). Griffis et al. (2004b) have estimated δR based on two-level gradient measurements of 12CO2 and 13CO2 using the TDL technique. This gradient approach (also referred to as the flux ratio method) can be used to obtain short-term, dynamic estimates of δR and is less dependent on the variation of the background atmosphere. Their study carried out over a harvested agricultural ecosystem (Griffis et al. 2004b) showed that the gradient approach generally agreed well with the Keeling plot method on δR estimation but had larger uncertainty because of the relatively small fluxes during the measurement period (November in Minnesota). However, this method requires further testing during growing season conditions when fluxes are greater.

Therefore, the objectives of this paper are: (1) to examine the short-term dynamics of δR and δN determined with the flux ratio method; (2) to partition FN of a C3–C4 rotation agricultural ecosystem using mass balance principles by combining TDL and micrometeorological measurements; and (3) to explore the uncertainties of the isotopic partitioning approach and present recommendations for future studies.


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  9. Appendices


The experiment was conducted in a 17 ha corn (Zea mays L., C4 photosynthetic pathway) field from 21 May to 14 October [day of year (DOY) 141–287] 2003 at the Rosemount Research and Outreach Center of the University of Minnesota, 24 km south of St. Paul (44°42′N, 93°05′W, elevation of 259.8 m.a.s.l.). The pre-settlement vegetation of the site was upland dry prairie, with conversion to agriculture occurring approximately 125 years ago (Griffis, Baker & Zhang 2005). The site, which had been in continuous corn production during the previous 4 years, was planted with soybeans (Glycine max, C3 photosynthetic pathway) in 2002. The site is flat and homogenous with a fetch of about 200 m in all directions. The soil is predominantly a Waukegan silt loam with an average bulk density of 1.25 g cm−3. The isotopic composition of the soil organic matter ranges from about −15.1‰ at a depth of 90 cm to −18.0‰ at a depth of 5 cm (Griffis et al. 2005).

Micrometeorological measurements

The details of the instrumentation and field set-up have been well documented by Griffis et al. (2004b) and Baker & Griffis (2005). The mixing ratios of 12CO2 and 13CO2 (µmol CO2 mol−1 dry air) were measured with the TDL technique (TGA100, Campbell Scientific Inc., Logan UT, USA). The instrument was maintained in a temperature-controlled research trailer approximately 200 m from the instrument tower. Three air inlets, one inside the canopy and two above the canopy, were mounted on the tower and were connected with Synflex tubing (Synflex Type 1300, Aurora, OH) to the TDL manifold. Each air inlet was composed of a Delrin 25 mm filter with Teflon filter membranes (A-06623-32 and EW-02916-72, Cole-Parmer, Vernon Hills, IL, USA) and a brass critical flow orifice (model D-7-BR, O’Keefe Controls Co., Monroe, CT, USA) that controlled the flow rate at 0.260 L min−1. The heights of the inlets were adjusted according to canopy development, but the separation between the two inlets above the canopy remained at 0.65 m over the experimental period. Air was pulled through a Nafion Dryer (PD-200T-24SS, Perma Pure Inc., Toms River, NJ, USA) into the TDL sample cell by a vacuum pump (Busch Rotary Vane Vacuum Pump, RB0021-L, Busch Inc., Shropshire, UK). A solenoid manifold, controlled by the TDL software, was used to select each intake line. A CO2 reference gas with approximately 10%12CO2 and 1%13CO2 flowed through the reference cell at a rate of 10 mL min−1. The reference cell signal is used only to provide a spectral template, thus the concentration need not be known with high precision. Two gases with known total CO2 mixing ratio (351.84 and 657.11 µmol mol−1) and isotope ratio (−14.43 and −14.36‰) were used to calibrate the TDL every 2 min. These working standards were propagated by using NOAA-CMDL primary standards to calibrate unknown cylinders for mixing ratios of isotopomers with the TDL (Griffis et al. 2004b). The sampling algorithm cycled through two calibration gases and then four air inlets (the fourth inlet was positioned for zero gradient testing) in 2 min. Each line was sampled for 20 s at 10 Hz, with the first 7 s of measurement omitted for pressure equilibration and the next 13 s of measurement averaged as the mean of the 2 min period. Small sample cell pressure differences between the calibration tank and the field inlets were observed. The average sample cell pressure of the two inlets measured above the canopy over the entire period was approximately 14.4 and 16.9 Pa, respectively. Pressure testing indicated that the effect of pressure fluctuation on the isotope ratio measurement was random, about 0.0059‰ per Pa. Thus, the observed pressure difference between the calibration tank and the field inlets would cause a ± 0.08‰ and ± 0.10‰ variation on the 2 min δa measurement for the two inlets above the canopy, respectively, and a negligible influence on the δN and δR estimated with the flux ratio method (< 0.001‰).

A 3-D sonic anemometer–thermometer (CSAT3, Campbell Scientific Inc.) and an open-path infrared gas analyser (LI-7500, Li-Cor Inc., Lincoln, NE, USA) were mounted on the same tower as the TDL sample inlets. The EC system was positioned at a height of 2 m above the ground when the canopy was less than 1 m high. The height of the EC system was then adjusted upward as the crop grew. For most of the experimental period, the EC system was at the centre of the two TDL inlets above the canopy. The fluxes of sensible heat (H), latent heat (λE) and CO2 were derived from the half-hourly mean covariance of the fluctuation of vertical wind speed (w′) and the fluctuations of air temperature (Ta′), water vapour density (q′) and CO2 concentration (C′), respectively. The EC system sampled all signals at 10 Hz and stored half-hourly statistics to a datalogger (Campbell CR23X, Campbell Scientific Inc.).

Downwelling and upwelling solar and long-wave radiation were measured with upward- and downward-facing pyranometers and pyrgeometers, respectively (models 8–48 and PIR, Eppley Laboratory Inc., Newport, RI, USA), mounted in close proximity at a height of 3 m from the soil surface. Net radiation (Rn) was computed as the sum of these four component measurements. Soil heat flux was measured with two self-calibrating heat flux plates (HFP01SC, Hukseflux Thermal Sensors, Delft, the Netherlands) at a depth of 10 cm. The mean soil temperature in the 10 cm layer above the heat flux plate was averaged from the measurements of three thermocouples buried at depths of 1.5, 5 and 8.5 cm. The soil heat capacity was measured by a dual needle probe custom made by Thermal Logic Devices (Pullman, WA, USA). The soil heat flux was corrected for heat storage in the top 10 cm layer. The radiation and heat flux data were recorded on a separate datalogger (Campbell 21X, Campbell Scientific Inc.). Weekly leaf area index (LAI) was measured with an AccuPAR handheld sensor (AccuPAR, Model PAR-80, Decagon Devices Inc., Pullman, WA, USA).

Analysis of plant carbon isotope ratio

Green corn leaves were collected every 2 weeks for isotope analysis. Fifteen plants were randomly collected from three plots. The leaves were cleaned and oven dried at 60 °C for at least 48 h until the mass remained constant. Samples were ground to a fine powder with a ball mill (5300 Mixer/Mill, Spex Industries, Edison, NJ, USA). A subsample of approximately 2 mg was weighed into a foil capsule and analysed for the isotope ratio on a continuous flow model mass spectrometer (Optima, Waters Corporation, Milford, MA, USA). The isotope analysis was expressed as an isotopic ratio δ (‰) relative to the Vienna Peedee Belemnite (VPDB) standard.

Flux partitioning

Mass balance principle

Based on the principle of mass balance, FA, FR and their isotopic components can be written after Bowling et al. (2001) as

  • FA+FR=FN(1)
  • (δa−Δcanopy) · FA+δR · FR=δ N · FN(2)

where FN is directly measured by the EC approach on the assumption that the rate of change of CO2 storage between the ground and the measurement height is negligible for turbulent conditions (friction velocity u* ≥ 0.1 m s−1). A positive sign indicates a flux leaving the surface and a negative sign indicates a flux towards the surface. δR and δN are the isotope ratios of respired CO2 and the net exchange of CO2 between the surface and the atmosphere, respectively. Δcanopy is the whole-canopy photosynthetic discrimination. To solve for FA and FR in Eqns 1 and 2, it is necessary to determine the parameters δR, Δcanopy and δN.

Isotope ratio of ecosystem respiration and net ecosystem CO2 exchange

δR was estimated with the flux ratio method according to Griffis et al. (2004b),

  • image(3)

where the superscripts 13 and 12 represent 13CO2 and 12CO2, respectively. Kc is eddy diffusivity, dinline image/dz indicates the time-averaged mixing ratio gradients of 13CO2 and 12CO2 measured simultaneously at two heights above the canopy and Ma is the molecular weight of dry air. By assuming similarity in the KC for 12CO2 and 13CO2, the flux ratio reduces to inline image, from which δR can be derived using night-time data as:

  • image(4)

where Rstd is the standard molar ratio (see appendix I in Griffis et al. 2004b for details). The nightly flux ratio, inline image, was obtained from the slope of a geometric mean regression between the 2 min measurements of 13CO2 and 12CO2 made over the entire night. Periods of weak turbulence (u* < 0.1 m s−1) were screened out. For comparison, δR was also estimated with the Keeling plot method at the first inlet above the canopy. During the growing season conditions, the flux ratio method cannot estimate daytime δR and the Keeling plot method is subject to errors caused by variation of convective boundary layer isotope composition and the influence of photosynthetic activity (Bowling et al. 2001; Pataki et al. 2003). Therefore, we assumed that the daytime δR could be interpolated from two neighbouring night-time periods. This assumption may be violated when there are significant differences in the isotope ratio between the heterotrophic and autotrophic components of respiration.

Similarly, δN was estimated with the flux ratio method using 2 min data collected during the daytime. Hourly δN values were obtained using measurements made during the previous and the following half-hours and were interpolated into half-hourly values.

Canopy-scale photosynthetic discrimination

By assuming an analogy between the leaf and the canopy-scale photosynthetic discrimination, Δcanopy was determined with the following equations (Farquhar, Ehleringer & Hubick 1989; Bowling et al. 2001):

  • FA=gc(CaCi)((5.1) )
  • Δcanopy=a+ (b4+b3φa)
  • image((5.2) )

where Ci and Ca are the mixing ratios of the canopy averaged intercellular CO2 and the ambient CO2 at the lower inlet above the canopy, respectively. The canopy bulk stomatal conductance for CO2 (gc) was inverted from the Penman–Monteith (PM) equation (Appendix I). Parameter a is the discrimination caused by diffusion through the stomata (about 4.4‰), b3 and b4 are the discrimination factors related to RuP2 carboxylation (27‰) and PEP carboxylase (−5.7‰), respectively, and φ is the fraction of CO2 leaking out of the bundle sheath cells and refixed by Rubisco. Literature values of φ generally range from 0.2 to 0.5, largely dependent on the anatomical characteristics of leaves and the mesophyll and bundle sheath activities (Hattersley 1982; Evans et al. 1986; Farquhar et al. 1989). Here, φ was constrained from the isotope ratio of top plant leaves (11.8 ± 0.4‰) and Eqn 5.2, which appeared to be approximately 0.3 by assuming a typical Ci/Ca value of 0.3. We assumed that the leaf-scale values of a, b3, b4 and φ could be applied to the canopy scale (Fung et al. 1997; Bowling et al. 2001), and obtained the following by rearranging Eqns 5.1 and 5.2:

  • image((5.3) )

where b′=b4+b3φ– a. δR and δN were determined directly from measurements. This leaves three unknowns –FA, FR and Δcanopy– in the non-linear equation set composed of Eqns 1, 2 and 5.3, allowing an analytical solution. The isotope ratio of the assimilated CO2 by photosynthesis (δP) was derived from Δcanopy= (δaδp) / (1000 +δp).

Ecosystem respiration estimated from night-time regression

Ecosystem respiration (Re) is traditionally estimated with night-time EC data collected under turbulent conditions or with chamber measurements. These data are typically used to develop seasonal or annual relationships between the night-time FN and soil temperature (Ts) and soil water content (Lloyd & Taylor 1994; Black et al. 1996; Lavigne et al. 1997; Janssens et al. 2001; Barr et al. 2002). The night-time FN showed an exponential relationship with Ts measured at a depth of 2.5 cm. The night-time FN also increased exponentially with LAI, which was used as a surrogate for the influence of phenology, productivity and increased availability of substrates for respiration. From the foregoing observations, we developed a non-linear regression model for Re as follows:

  • Re=Aexp(B1Ts+B2LAI) · f(θ)((6.1) )
  • image((6.2) )

Empirical parameters A, B1 and B2 were determined with an optimization method. θ is the volumetric soil water content at 10 cm depth, and θ0 is the optimal soil water content, which appeared to be 0.24 m3 m−3 for our soil. LAI was simulated with a polynomial regression of measured LAI and time, and Ts and θ were all measured half-hourly. Data collected for u* ≥ 0.1 m s−1 were used to optimize the parameters A, B1 and B2. The regression model explained 66% of the total variance of the measured night-time FN.


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  9. Appendices

Climate and phenology

The Ts, cumulative precipitation, soil water content and LAI during the growing season are shown in Fig. 1. Soil temperature at the 2.5 cm depth reached a maximum around DOY 166 (Fig. 1a). The summer of 2003 was relatively dry, with only four rain events ≥ 10 mm. Total precipitation from DOY 121–274 (1 May to 31 September) was 400 mm (Fig. 1b), which was 26% less than the 30-year (1971–2000) climate normal. Soil water content remained relatively low over much of the measurement period (Fig. 1c), ranging from 0.16 to 0.34 m3 m−3, and generally remained < 0.23 m3 m−3 late in the growing season after the corn had tasselled. The corn emerged around DOY 135 (15 May) and was harvested on DOY 287 (14 October). The maximum LAI was 4.5 m2 m−2, observed on DOY 219 (8 August). Critical growth stages (defined in Ritchie, Hanway & Benson 1993) were observed as follows: (1) from emergence to nine-leaf stage (DOY 135–176); (2) from nine-leaf to tassel stage (DOY 177–206), which was the rapid vegetative growth stage; (3) silking and blister (DOY 207–225); and (4) from milk to physiological maturity (DOY 226–257).


Figure 1. Climate and phenology in 2003: (a) soil temperature at 2.5 cm depth; (b) cumulative precipitation; (c) soil water content at 10 cm depth; and (d) measured leaf area index (LAI) (circles) and simulated LAI (solid line), where the growth stages are indicated by dotted lines.

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Diurnal variation of the CO2 mixing ratio and carbon isotope ratio of ambient air

Figure 2 shows the ensemble diurnal variation of half-hourly CO2 mixing ratio and the isotope ratio during typical days (DOY 210–217). The average canopy height was 2.8 m, and the corn canopy had just tasselled. The daytime CO2 mixing ratio was relatively low, in the vicinity of 350 µmol mol−1 (Fig. 2a). The CO2 mixing ratio began to increase after sunset at around 1900 h and reached a maximum at midnight. The range of daytime CO2 mixing ratio was small, typically less than 40 µmol mol−1, while the range at night was often greater than 100 µmol mol−1.


Figure 2. Ensemble diurnal variations of CO2 mixing ratio and isotope ratio during day of year (DOY) 210–217 (29 July to 5 August). (a) mixing ratios of CO2 at three heights, two above the canopy and one inside the canopy; and (b) isotope ratios of ambient air at the three heights. Daytime details are shown in the magnified inset figures.

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The effects of photosynthesis and respiration on atmospheric 13CO2 abundance were also indicated in the temporal variation of the isotope ratio (Fig. 2b). During the daytime, air was enriched in 13CO2 because of photosynthetic discrimination, and the isotope ratio was relatively high, about −7.6‰. At night, the values were more negative as a result of respiration and were typically around −10.6‰. Similar diurnal patterns of CO2 mixing ratio and isotope ratio were observed by Buchmann & Ehleringer (1998) over a corn canopy.

The differences in CO2 mixing ratio and isotope ratio among the three measurement heights were most evident at night. During the day, the differences were relatively small but significant (i.e. greater than the measurement precision of the TDL, see Griffis et al. 2004b). The inlet inside the canopy (1.0 m from the ground) typically measured the lowest CO2 mixing ratio and the most negative isotope ratio. The daytime relative depletion of 13CO2 inside the canopy was most likely a result of ecosystem respiration. Light attenuation may also cause 13CO2 depletion through increasing Ci/Ca (and thus photosynthetic discrimination). However, this effect is estimated to be small for C4 plants according to Eqn 5.3 and Farquhar et al. (1989).

Canopy bulk stomatal conductance for CO2

The determination of gc is critical to flux partitioning because it is directly related to the photosynthetic computation (Eqn 5). Unfortunately, the gc estimated with the PM equation can involve relatively large uncertainties resulting from lack of energy balance closure, the generally unknown contribution of soil evaporation and errors associated with EC measurements. To limit these problems, we forced energy balance closure using the Bowen ratio obtained from the EC measurements (Twine et al. 2000), and limited our analysis to turbulent conditions when the canopy was dry (83% of the data). During the full canopy period (LAI ≥ 2), soil evaporation accounted for 3–10% of the total canopy evapotranspiration, leading to an overestimation of 1.2–12% of gc (Appendix II). The uncertainty in gc, caused by measurement errors in H, λE, wind speed (u) and water vapour pressure deficit (VPD) was estimated to be approximately 30% (see Appendix II for the details of uncertainty analysis).

Figure 3 shows the ensemble diurnal variations of gc. Maximum gc was observed during the rapid vegetative growth stage (Fig. 3a), about 0.5 mol m−2 s−1. Late in the growing season, gc decreased to less than 0.2 mol m−2 s−1 (Fig. 3c). These values are in good agreement with other studies (Kelliher et al. 1995; Steduto & Hsiao 1998). For most of the experimental period, the daily maximum gc tended to skew towards the morning, which is typical for a canopy that is water stressed (Steduto & Hsiao 1998; Kurpius et al. 2003).


Figure 3. Ensemble diurnal variation of gc during critical growth stages. Error bars represent the standard error of the mean.

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Isotope ratio of ecosystem respiration

The uncertainties in the flux ratio and Keeling estimates of nightly δR using 2 min data collected over the entire night are shown in Table 1. The uncertainty of the flux ratio estimate was typically 0.7‰, which was larger than the Keeling estimate of about 0.4‰. The uncertainties of both methods increased significantly as the range of CO2 mixing ratio decreased, an occurrence that has also been reported in other studies (Pataki et al. 2003). For instance, to limit the uncertainty to within 3‰, the Keeling method required ≥ 10 µmol mol−1 range of CO2 mixing ratio (about 99% of the night-time observations met this threshold), and the flux ratio method required ≥ 10 µmol mol−1 range of CO2 mixing ratio difference between the two inlets (about 92% of the night-time observations met this threshold).

Table 1.  The uncertainties in the estimation of nightly δR. The uncertainty of the Keeling estimate is the standard error of the intercept. The uncertainty of the flux ratio estimate is calculated as (standard error of the slope / Rstd) × 1000 (‰). Two-minute data collected over the entire night when u* ≥ 0.1 m s−1 were used for both methods
StatisticsFlux ratioKeeling interceptUnits
  • a

    The range of the difference in CO2 mixing ratio between the two intakes above the canopy.

r2> 0.990.8
Standard error0.70.4
CO2 range40a102µmol mol−1

Night-time hourly δR obtained with the flux ratio method showed considerable variations, with values typically fluctuating by about 2.0‰. Bowling et al. (2003) also reported significant hourly variation of up to 6.4‰ for δR in a grassland. For a typical nocturnal pattern, hourly δR values decreased with time and reached a minimum value before sunrise. There are two possible explanations for this observation. Firstly, the isotopic composition of rhizosphere respiration may have become more depleted during the night as the substrates that were assimilated during the daytime were consumed and microbes switched to other available substrates that were less enriched. Secondly, as the night progressed, the above-ground foliar respiration could have been inhibited more than the below-ground heterotrophic respiration as a result of decreasing air temperature or substrate availability. Both mechanisms could cause δR to become relatively more depleted over the course of the night. The considerable hourly variation of night-time δR implies that there might be important limitation on the extrapolation of night-time δR to daytime values in the isotopic flux partitioning. Daytime chamber measurements on the individual component of ecosystem respiration are needed to examine this issue in further detail.

The flux ratio and the Keeling estimates of nightly δR are shown in Fig. 4. On average, the Keeling method tended to give lower values particularly during the full canopy closure period (LAI ≥ 2, DOY 177–257). One possible explanation for the discrepancy is the fetch mismatch between the two methods. A footprint analysis (Schuepp et al. 1990) showed that the effective fetch of the mixing ratio measurement at night was typically > 270 m, which was larger than the 200 m fetch of the site. It is possible that the advection of depleted CO2 from the surrounding C3 vegetation (forests and some agricultural crops) and combustion sources had influenced the mixing ratio measurements, resulting in lower Keeling estimates. In comparison, the flux measurement (derived from mixing ratio gradient) typically had an effective fetch of less than 150 m, implying that the influence of advection on the flux ratio method was smaller.


Figure 4. Seasonal variation of δR in 2003. Error bars indicate the uncertainties (standard errors) of the flux ratio and Keeling estimates, respectively.

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Another possible reason for the difference is the variation of boundary layer atmospheric CO2. As CO2 is respired and mixed into the nocturnal boundary layer, the mixing ratio and the isotope ratio of ‘background CO2’ (Cbg = Ca −CR, where CR is the mixing ratio of respired CO2) varies over the course of the night. In addition, it is possible that advection from C3 vegetation or combustion sources could have affected the ‘background CO2’ considerably. This temporal variation of boundary layer CO2 introduces a bias into the night-time Keeling estimates. We hypothesized that at an hourly timescale the changes in the nocturnal boundary layer characteristics are smaller and have less influence on the Keeling estimates. We observed that the nightly Keeling estimates were generally 2‰ lower than the hourly values averaged over the entire night (hourly estimates with a standard error of σ < 1‰ were used). The flux ratio estimates did not show such significant difference between the hourly and nightly values. For hourly δR values, the flux ratio and the Keeling methods showed a typical difference of 1.7‰, which is smaller than the 3.5‰ difference for nightly values. At this point, the influence of background CO2 variation on the Keeling estimates cannot be evaluated directly. Boundary layer modelling is needed to explore this issue in greater detail. Taking into account the possible influence of advection and background CO2 on the Keeling plot and to be consistent in terms of footprint match with FN and δN, we used the flux ratio method for nightly δR in the following partitioning.

Considerable seasonal variation in night-time δR was observed (Fig. 4). During the spring (DOY < 160), values fluctuated between approximately −32 and −19‰, and then increased rapidly to a maximum of approximately −11‰ in early August (around DOY 214) before declining in the fall (> DOY 255) to values in the range of −32 to −20‰. This seasonal variation of δR was strongly related to the canopy development, as indicated by a linear relationship with LAI (r 2 = 0.64, P < 0.001). We hypothesized that the higher values during DOY 182–243 (July to August) were largely attributable to the increase in the more enriched autotrophic respiration of the C4 corn. Lai et al. (2003) has also reported impacts of phenology on seasonal variation of δR over a mixed C4–C3 grassland, where δR did not show distinct temporal pattern because of the changes in C3 and C4 contributions. The rapid decline in δR at the conclusion of the growing season was somewhat unexpected. However, during this period (DOY 255–263), a rain event increased the θ from 0.2 to 0.25 m3 m−3. Soil temperature at 2.5 cm depth also increased from 10 to > 20 °C (data not shown). The relatively warm, moist conditions likely stimulated heterotrophic respiration, causing a decrease in δR.

δR has also been shown to be influenced by precipitation, soil water content and VPD (Ehleringer & Cerling 1995; Bowling et al. 2002; Ometto et al. 2002; Fessenden & Ehleringer 2003; Lai et al. 2004; McDowell et al. 2004), which could explain some of the large day-to-day variations in δR. For instance, the abnormally low values of δR on DOY 235, 255 and 262 were preceded by rain events within 48 h. However, the low values of δR on DOY 190 and 198 were not related to θ or precipitation. Those days were characterized by low air temperature and low solar radiation, both of which would be expected to have a greater negative impact on the above-ground foliar respiration than the below-ground heterotrophic respiration. In addition, the reduced carbon assimilation, partly reflected in the low FN values, might also limit autotrophic respiration.

Isotope ratio of net ecosystem CO2 exchange and photosynthetic discrimination

Figure 5 shows the ensemble δR and δN estimated with the flux ratio method. The figure also shows Δcanopy and the isotopic ratio of the canopy photosynthesis (δP) obtained after FA was partitioned. δN depends on the magnitude of FN, δR and Δcanopy. It is therefore not surprising that relatively large fluctuations were observed in δN. For the majority of the daytime values, δN varied between −12 and −4‰. The Δcanopy remained relatively constant both diurnally and seasonally in the vicinity of 3‰, which was smaller than the value of approximately 4‰ deduced from the difference between the measured plant isotope ratio (top leaves −11.8 ± 0.4‰, bottom leaves −12.3 ± 0.3‰) and the mean ambient air ratio of −7.8‰. The relatively constant Δcanopy resulted from the positive contribution of PEP carboxylase to the assimilation of 13CO2, about −5.7‰ in terms of discrimination.


Figure 5. Ensemble diurnal variations of δR (solid line), δN (dotted line with circles), δP (dot-dashed line), δa (solid line with points) and Δcanopy (dashed line).

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The Δcanopy is an important factor in some biophysical models (e.g. SiB2) that are used to partition the carbon budget at the global scale (Ciais et al. 1995; Fung et al. 1997). Fung et al. (1997) showed that a change of 3‰ in annual mean Δcanopy could cause a 0.7 Gt C year−1 bias in the carbon sink. Here, the estimate of Δcanopy is smaller than the global mean value of 3.6‰ for C4 plants reported by Lloyd & Farquhar (1994). While the Δcanopy remained relatively stable in our study, the Δcanopy of C3 or mixed C4–C3 ecosystems typically shows significant diurnal and seasonal variations resulting from changes in Ci/Ca. Lai et al. (2003) observed an apparent diurnal pattern of Δcanopy ranging from about 0.7‰ in the morning and evening to approximately 2.8‰ at midday over a mixed C4–C3 grassland. Bowling et al. (2001) also observed a strong diurnal variation of Δcanopy, approximately 16 to 19‰ over a temperate deciduous forest.

Partitioning net ecosystem CO2 exchange into photosynthesis and respiration

Half-hourly FN was partitioned into photosynthesis and respiration using both the isotopic approach and the regression method for the full canopy period. The diurnal ensemble partitioning for each growth stage is shown in Fig. 6. In general, FA ranged between −30 and −50 µmol m−2 s−1, and FR typically varied from slightly above zero to 15 µmol m−2 s−1. These results are consistent with other values in literature (Grant et al. 1989; Pattey et al. 1991; Steduto & Hsiao 1998). Both FA and FR peaked during the silking to blister stage (DOY 207–225) (Fig. 6b). The isotopic flux partitioning generally showed larger half-hourly variability than the regression method. The differences between the two methods were particularly significant at around midday, when FR sometimes showed depressions while Re continued to increase with time. No significant relationship between Re and FR was observed from 1:1 plots (figures not shown).


Figure 6. Ensemble diurnal variations of photosynthesis and respiration from the isotopic partitioning method and night-time regression method during critical growth stages. The shaded area and error bars indicate the standard error of Re and FR, respectively.

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We note that the daytime pattern of Re is a direct consequence of the soil temperature and water content changes and might not represent the true physiological response of the ecosystem. Studies suggest that the night-time regression method might considerably overestimate the daytime respiration by up to 15% without considering the photoinhibition effect of photosynthesis on foliar respiration (Kok effect) (Brooks & Farquhar 1985; Janssens et al. 2001). The values of FR, however, were sometimes unrealistically low during midday (Fig. 6a & b). This might be related to the uncertainties associated with the TDL and micrometeorological measurements (discussed in further detail below). It is also important to note, however, that the isotopic flux partitioning based on mass balance principle might have considerably underestimated the photosynthesis and respiration without considering the process of CO2 recycling inside the canopy (Greaver et al. 2005).

Uncertainty analysis of isotopic flux partitioning and future recommendations

Unrealistic isotopic partitioning, that is, unrealistic values of FR, were observed, indicating that there are important uncertainties in the micrometeorological-stable isotope technique that require further investigation. For example, at around 1130 h in Fig. 6b and 1230 h in Fig. 6c, the partitioned FR was apparently below zero. In addition, the particularly high values of FR, about 15 µmol m−2 s−1, at around 1200 and 1300 h shown in Fig. 6c were unreasonable for the late growing season. These failed cases were usually associated with very low δN values, high daytime δR values, or in some cases, the unreasonably high or low gc values, assuming FN to be the ‘true’ value. Considering the magnitude of errors typically involved in the half-hourly micrometeorological measurement, which could be up to 30%, and the uncertainties in the half-hourly TDL values of δN and δR, we should not be surprised by the relatively large errors in the isotopic flux partitioning.

The total uncertainty in the partitioning of FA, propagated from errors of individual variables, was calculated according to Bevington (1969) (see Appendix II for the details of error propagation). Results showed that the total uncertainty was typically around 30% in the early growth season and increased to > 40% for the mid and late seasons when the difference between the isotope ratio of photosynthesis and respiration was small or otherwise the fluxes were small. An uncertainty test was therefore performed to examine the contribution of each variable to the total uncertainty. In order to identify the influence of isotopic disequlibrium or inline image, we selected the early and mid seasons as two examples for which the mean δR was assigned to be −20 and −14‰, respectively. The mean values and uncertainties of Ca, gc, δN and δa were assigned constant values (Table 2). The individual contributions are shown in Table 3, which also shows the partial derivatives evaluated at the mean values. These partial derivatives indicate the sensitivity of FA to each variable.

Table 2.  The means and uncertainties of the individual variables used in the uncertainty test. The uncertainties of Ca and δa are the measurement precisions of tunable diode laser (TDL) (Griffis et al. 2004b). The uncertainty of δN is the standard error of the flux ratio estimate. The uncertainty of δR is the hour-to-hour variability of night-time values
VariableMean valuesUncertaintiesUnits
  • a

    Mean values of δR in early/mid growing seasons.

  • bFN was assumed to be the ‘true’ value.

gc0.30.09mol m−2 s−1
Ca3500.03µmol mol−1
FN−250bµmol m−2 s−1
Table 3.  Contributions of individual variables to the total uncertainty in FA. pi represents the contribution of individual variable xi to the total uncertainty. The typical mean value x0 and the uncertainty of each variable are given in Table 2
Variable xiEarly seasonMid season
pi (%)inline imagepi (%)inline image
Ca< 0.01< 0.01< 0.01< 0.01

The results indicated that the uncertainties in δN estimates imposed the most significant influence on the partitioning, accounting for more than 80% of the total uncertainty (Table 3). The partitioning was also highly sensitive to δN, with a 1‰ fluctuation in δN resulting in a 10 and 25% change of FA for the early and mid season, respectively. As reported in other studies, the precise estimation of δN (or isoflux δN · FN) is essential to the isotopic flux partitioning (Bowling et al. 2001; Lai et al. 2003; Ogée et al. 2003, 2004). In this study, the uncertainty in the hourly flux ratio estimate of δN was large, ranging from 0.5 to 6‰ because of the relatively small differences in the CO2 mixing ratios between the two inlets during the daytime (< 1.5 µmol mol−1). The precision of δN could be improved by increasing the separation between the two measuring levels to obtain larger gradients in 12CO2 and 13CO2 or by extending the sampling period. Buffer volumes could be used to reduce the noise caused by turbulent fluctuations in the TDL measurements of 12CO2 and 13CO2. The uncertainty in FA could also be reduced by measuring the flux of 13CO2 directly with EC, by which the problems related to footprint mismatch and small gradient on the isoflux estimation would be overcome. For instance, the total uncertainty in FA will decrease by approximately 50% for both the early and mid growing seasons (according to the values in Table 2 and by considering δN × FN as a single variable), if the assumption of 20% error for the 13CO2 flux measurement is made.

The fluctuation in δR also contributed considerably, though much less than δN, to the total uncertainty (Table 3). The uncertainty in δR accounted for approximately 17% during the mid season when the isotopic disequlibrium was small (≈ 3‰), and about 2% early in the growing season when the disequilibrium was large (≈ 9‰). Based on the

sensitivity of the partitioning to δR[inline image in

Table 3], the 2‰ difference between the hourly flux ratio and the Keeling estimates of δR resulted in an approximate 4% change in FA in the early season and up to > 30% variation in the mid season when the isotopic disequilibrium was relatively small.

The gc estimate was expected to involve large uncertainties (see Appendix II). However, the contribution of gc errors to the total uncertainty varied considerably with the errors of other variables. For instance, the error in gc accounted for less than 1% of the total uncertainty when the uncertainties of δR and δN were relatively large (i.e. > 2‰). The error in gc accounted for more than 25% when the uncertainty of δR and δN was limited to within 0.5‰.

The influence of isotopic disequilibrium on flux partitioning is significant because the methodology will fail if δP equilibrates with δR. Ogée et al. (2004) showed that a small disequilibrium between δP and δR resulted in large uncertainties in the partitioning even after the precision of δR and δN was improved. Our results showed that the isotopic partitioning produced better results (indicated by less negative FR values) before DOY 185 when the difference between δP and δR was relatively large (> 5‰). According to the uncertainty analysis, the total uncertainty in FA increased from ≈ 30 to > 40% when inline image decreased from ≈ 9‰ in the early season to ≈ 3‰ in the mid season.

Although the partitioning showed high sensitivity to δa (Table 3), the instrumental errors in δa measurements are typically small and have a small influence (less than 0.1%) on the partitioning. The uncertainties associated with parameters a, b3 and b4 require further investigation and were not explicitly considered here. Nevertheless, the partitioning appears to be highly sensitive to these parameters. For instance, if the value of b3 is changed from 27 to 29‰, the FA would be altered by about 10% on average for all seasons. In addition, it is unlikely that φ will remain constant for different varieties of corn or for different environmental conditions. The assumption of the analogy between the leaf-scale and the canopy-scale discrimination needs further investigation. Leaf-scale measurements of isotopic exchange, stomatal conductance and photosynthesis, combined with physiological modelling, could provide additional insight into these issues.


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  9. Appendices

In this study, TDL measurements of 12CO2 and 13CO2 mixing ratios were combined with micrometeorological techniques to partition the net ecosystem CO2 exchange of a C3–C4 rotation agricultural ecosystem into photosynthesis and respiration on a half-hourly basis. We conclude that:

  • 1
    The ecosystem respiration partitioned with isotopic flux approach typically varied from about 0 to 15 µmol m−2 s−1 and the photosynthesis varied from about 30 to 50 µmol m−2 s−1 during the full canopy period. The isotopic approach generally showed greater variability than the night-time regression method and tended to give lower, and sometimes unrealistic, midday values.
  • 2
    The isotope ratio of night-time respiration showed significant seasonal variation from −32 to −11‰, corresponding with the seasonal development of the canopy. Night-time hourly variations of typically 2‰ were also observed. Therefore, the extrapolation of night-time values to the daytime represents a potentially important limitation to the isotopic flux partitioning methodology. The whole canopy photosynthetic discrimination remained relatively constant both diurnally and seasonally in the vicinity of 3‰. The isotope ratio of net CO2 exchange showed significant hour-to-hour variation within the range of −12 to −4‰.
  • 3
    The uncertainty in the isotopic flux partitioning methodology varied seasonally and diurnally. The largest source of uncertainty was related to the estimation of the isotope ratio of net CO2 exchange, or alternatively, the isoflux estimation. The isotopic flux partitioning could be considerably improved if the 13CO2 flux were measured directly using the EC technique. Furthermore, uncertainty in the isotopic partitioning was significantly reduced when the isotopic disequilibrium exceeded 5‰, which was observed at this site during the early growing season.
  • 4
    We expect that the isotopic flux partitioning approach could be greatly improved if the uncertainty in the flux ratio estimate of net ecosystem CO2 exchange was substantially reduced. We believe there is an opportunity to achieve this through the combination of the TDL and EC approach.


  1. Top of page
  9. Appendices

This research was supported by the Office of Science (BER), US Department of Energy, grant No. DE-FG02-03ER63684, and the University of Minnesota, Grant-in-Aid-of-Research, Artistry and Scholarship Program (TJG). The authors would like to thank the two anonymous reviewers and Dr Scott Saleska at the University of Arizona for their critical and constructive comments. We appreciate the field assistance of W.A. Breiter and K. Vang. Finally, we gratefully acknowledge the logistical support provided by the University of Minnesota, Rosemount Research and Outreach Center and the USDA-ARS.


  1. Top of page
  9. Appendices
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  9. Appendices


The canopy stomatal conductance for water vapour (gcw) was inverted from the Penman–Monteith equation:

  • image((A1) )

where ρ is the air density (kg m−3), Cp is the specific heat of air under constant pressure (J kg−1 K−1), β is the Bowen-ratio, λ is the latent heat of vaporization (J kg−1), E is the plant transpiration (mol m−2 s−1), γ is the psychrometric constant, s is the rate of change of saturation vapour pressure with temperature (Pa K−1) and VPD is the vapour pressure deficit (kPa). The aerodynamic conductance ga was determined from

  • 1/ga= 1/gb+ 1/ge((A2) )

where gb is the average boundary layer conductance of the canopy leaves, calculated according to Owen & Thompson (1963) and Verma (1989) as

  • 1/gb=B−1/u*((A3) )

where B−1 is the dimensionless Stanton number ge is the eddy diffusive conductance,

  • 1/ge =u/(u*)2((A4) )

where u is the average horizontal wind velocity (m s−1). The canopy stomatal conductance for CO2 (gc) was determined from gcw/(Dv/Dc), where Dv and Dc are the diffusion coefficients for water vapour and CO2 in air, respectively (Price & Black 1990).

When soil evaporation is considerably small, λE in Eqn A1 can be replaced with the latent heat flux measurement over the whole canopy. We used the Shuttleworth & Wallace (1985) two-layer model to estimate the contribution of soil evaporation. Results showed that the soil evaporation accounted for 3 to 10% during the period of full canopy closure (LAI ≥ 2), which as a result would cause a 1.2–12.2% overestimation in gc.


Uncertainty in gc estimation

The total uncertainty in the canopy conductance estimation (inline image) was propagated from the fluctuations in the individual variables, which was estimated following Bevington (1969),

  • image((A5) )

where xi, i = 1, 2, . . . 5, indicates the five key variables, VPD, λE, H, u and u*. σi denotes the uncertainty of variable xi. The uncertainties of individual variables are assumed to be uncorrelated, and the partial derivatives in the parentheses are evaluated at the mean values. The contribution of each variable to the total uncertainty (pi) is given by,

  • image((A6) )

The total uncertainty of gc was calculated half-hourly and pi is shown in Table 4.

Table 4.  Contributions of individual variables to the total uncertainty in gc estimation. The uncertainty of u is taken as the precision of wind speed measurement from the CSAT3 sonic anemometer. The uncertainty of water vapour pressure deficit (VPD) is estimated from the precision of water vapour density measurement from the LI-7500 (2.41e-06 kg m−3) using the ideal gas law. Uncertainties of fluxes are estimated to be 20% (Morgenstern et al. 2004). The uncertainty of u* is estimated as inline image, where FM = inline image and inline image.
Variable xiContribution pi (%)
u< 0.001

The total uncertainty in gc was typically 30% during the experimental period. The uncertainties in VPD and λE contributed the most to the total error, about 54% and 45%, respectively.

Uncertainty in isotopic flux partitioning and night-time regression model

Similarly, the total uncertainty in the isotopic partitioning (inline image) was calculated as,

  • image((A7) )

where xi denotes the variable examined here: δa, δN, δR, gc and Ca. Although FN can be associated with relatively large error, here we assume it represents the ‘true’ value.