Stable isotopes act as tracers for studying flows of material through ecosystems and the atmosphere (Farquhar, Ehleringer & Hubick 1989; Ehleringer, Hall & Farquhar 1993; Flanagan & Ehleringer 1998; Yakir & Sternberg 2000). In practice, ecologists and biogeochemists use information on the stable carbon isotope content of air, plants and soil to provide information on: (1) plant water use efficiency (Farquhar & Richards 1984; Farquhar et al. 1988; Condon, Richards & Farquhar 1993; Hall, Ismail & Menendez 1993); (2) recycling of respired carbon dioxide within forests (Schleser & Jayasekera 1985; Sternberg 1989; Lloyd et al. 1996; Sternberg et al. 1997; Yakir & Sternberg 2000); (3) the partitioning of net ecosystem carbon exchange into its components, photosynthesis and respiration (Yakir & Wang 1996; Bowling, Monson & Tans 2001); (4) identifying and quantifying the distribution and contributions of C3 and C4 species to global primary productivity (Lloyd & Farquhar 1994; Ehleringer, Cerling & Helliker 1997; Sage, Wedin & Li 1999); and (5) the partitioning of CO2 exchange between terrestrial biosphere and oceanic reservoirs in global carbon cycle models (Ciais et al. 1995; Fung et al. 1997).
Plant material and the CO2 respired by plants or the decomposition of plant material are depleted in 13C relative to that in the atmosphere. This depletion is due to discrimination against CO2 molecules containing the heavier isotope, 13C, when molecules diffuse across the laminar boundary layer of leaves and are carboxylated by the enzyme Rubisco during photosynthesis (Farquhar et al. 1989; O’Leary, Madhaven & Paneth 1992; O’Leary 1993; Lloyd & Farquhar 1994; Yakir & Sternberg 2000). Other discriminating processes include the hydration of CO2, and the diffusion of CO2 in aqueous solution (O’Leary 1993). The isotopic signature of respiring roots, soil microbes and leaves, on the other hand, differ from one another due to their unique turnover times (Flanagan & Ehleringer 1998). Each respiring carbon pool possesses a different isotopic content because the isotopic content of the atmospheric CO2 fixed by the plants is decreasing with time; fossil fuel combustion is diluting the isotopic content of the atmosphere because it is oxidizing organic compounds that are depleted in 13C, due to their photosynthetic origin (Francey et al. 1995). Consequently, carbon in older pools generally contains more 13C than carbon that was assimilated more recently. Other factors leading to variation in the 13C content of respiration include selective degradation of various organic compounds by microbes, leaching of soluble organic components, and refixation of diffusively enriched CO2 within the soil gas (Gleixner et al. 1998; Ehleringer, Buchmann & Flanagan 2000).
Isotopic mixing lines, called ‘Keeling plots’ (Keeling 1958), are used to quantify the carbon isotope composition of respiring sources, such as an ecosystem and soil (Flanagan et al. 1996; Buchmann & Ehleringer 1998; Yakir & Sternberg 2000; Bowling et al. 2002; Pataki et al. 2002). In principle, a respiring source changes the ambient CO2 mixing ratio and its isotopic composition. The isotopic composition of the respiring source can be deduced from the two end-member mixing relationship, on the assumption that a canopy is a well-mixed vessel (Keeling 1958). However, plant canopies are not well-mixed vessels. Drag and shear imposed on the atmosphere by plants causes the turbulent transfer of trace gases between plants and the atmosphere to be intermittent and to occur against the mean scalar concentration gradient (Raupach, Finnigan & Bruwet 1996; Finnigan 2000). Furthermore, vertical variations in leaf photosynthetic capacity and canopy structure cause respiratory carbon fluxes to vary vertically throughout the canopy. Another source of variation associated with the measurement of Keeling plot intercepts arises from logistical and technological issues that compromise sampling frequency and density. Air samples must be collected in flasks and returned to a laboratory for analysis on a mass spectrometer. This time-consuming and expensive procedure limits the number of samples that can be collected and analysed during a given period, thereby producing a sample mean with a less than ideal sampling error. Quantitatively, the relative sampling error of an atmospheric trace gas concentration profile is a function of the time scale of turbulence, τ, and the time duration over which the entire profile is measured, Tc (Meyers et al. 1996):
From Eqn 1, we deduce that the relative sampling error equals 35% when the isotopic profile is sampled only once every 30 min and the turbulence time scale is 200 s. In contrast, a relative sampling error of less than 5% can be attained if the profile is sampled every minute; but this metric is not realistic when using a mass spectrometer at a distant laboratory. Implementing a less than ideal sampling frequency may be one source of variance associated with complex carbon isotope profiles reported in the literature (Medina & Minchin 1980; Schleser & Jayasekera 1985; Garten & Taylor 1992; Kruijt et al. 1996; Flanagan et al. 1996; Buchmann et al. 1997a; Buchmann, Kao & Ehleringer 1997b; Buchmann & Ehleringer 1998; LeRoux et al. 2001) and spatial variations of carbon dioxide sources and sinks may contribute to a controversy as to whether or not Keeling plot intercepts vary with time of day; the literature contains examples showing that the Keeling-plot intercepts for carbon isotopes do (Bowling, Baldocchi & Monson 1999a; Pataki et al. 2002) and do not change from night to day (Buchmann & Ehleringer 1998, Mortazavi & Chanton 2002).
In this article, we intend to evaluate carbon isotope measurements through the theoretical lens of a biometeorologist. Mechanistic biophysical models that couple micrometeorological and eco-physiological theories have the potential to shed light on how leaf-level relationships for isotopic discrimination can be integrated to the canopy and landscape dimensions. This capability exists because these models are able to resolve vertical profiles of carbon isotope discrimination with high vertical resolution and they can account for counter-gradient transfer (Katul & Albertson 1999; Lai et al. 2000; Baldocchi & Wilson 2001). Second, biophysical models can predict how isotope discrimination may respond to environmental perturbations. and third, biophysical models can produce information on the diurnal, seasonal and interannual dynamics of isotope discrimination. The value of this third feature stems from the fact that few long-term studies on isotope discrimination exist (e.g. Lowdon & Dyck 1974; Flanagan et al. 1996; Buchmann et al. 1997a, b; Damesin, Ramball & Joffre 1998; Bowling et al. 2002) due to the economic and logistical constraints of using mass spectrometers to analyse air samples.
Only a few biophysical models have been developed to assess stable carbon discrimination between a plant canopy and the atmosphere. To date, the majority of models have been developed for global scale applications (Lloyd & Farquhar 1994; Ciais et al. 1995; Fung et al. 1997). Of the models developed for studying carbon isotopic exchange in the surface boundary layer, two use ‘big-leaf’ theory (Lloyd et al. 1996; Bowling et al. 2001) and the others use Lagrangian localized near field (LNF) diffusion theory (Kruijt et al. 1996; Raupach 2001). ‘Big leaf’ models have self-acknowledged limitations. For example, they presuppose that a forest is physically and biochemically homogeneous, a false assumption in many circumstances as noted by reports of vertical gradients in isotopic discrimination (e.g. Garten & Taylor 1992; Buchmann & Ehleringer 1998). Lagrangian LNF theory has the potential to account for counter-gradient transfer. Yet, this modelling framework makes many simplifying assumptions about the heterogeneity of turbulence in the canopy (e.g. Warland & Thurtell 2000) and the quantification of sources and sinks. Furthermore, it ignores the effect of atmospheric stability on turbulent diffusion, which has an important impact on scalar fluxes and concentration fields inside canopies (Baldocchi & Harley 1995; Leuning 2000).
Biophysical models, such as CANOAK (Baldocchi & Harley 1995; Baldocchi 1997; Baldocchi & Wilson 2001), can be used to address many of the issues related to the interpretation of stable carbon isotopes in air and ecosystem components. First, CANOAK accounts for counter-gradient transfer and heterogeneous canopy turbulence by using a Lagrangian random-flight turbulent transfer scheme. Second, its multilayer architecture enables it to assess sources and sinks and trace gas, mixing ratios with high vertical resolution. These attributes give the model the potential to interpret Keeling plots intercepts during the day and night. Third, by coupling leaf energy balance, photosynthesis and stomatal conductance, CANOAK is able to examine interrelationships between water use efficiency, isotope discrimination and vapour pressure deficits with mechanistic detail. Fourth, its integration of algorithms that assess photosynthesis, stomatal conductance and radiative transfer through the canopy gives it the potential to diagnose how variations in canopy structure and photosynthetic capacity may alter isotope discrimination. and finally, by incorporating information on how leaf area index and physiological capacity vary over the growing season, a biophysical model, like CANOAK, has the potential to investigate how a forest canopy discriminates against 13C on daily, seasonal and yearly time scales.
In this paper, we describe adaptations that were made to the CANOAK model to enable it to simulate flux densities and concentration profiles of 13CO2 within and above a deciduous forest. We then compare model computations and measurements of isotopic fluxes and discrimination made during experiments at Walker Branch in 1998 (Bowling et al. 1999a, 2001). Finally, we discuss model computations were that performed to examine:
- 1vertical profiles and diurnal and seasonal patterns in whole-canopy carbon isotope discrimination (Δcanopy);
- 2the impact of variation in environmental variables (light, humidity deficits) on Δcanopy; and
- 3inter-relationships between Δcanopy, stand-level water use efficiency and humidity deficits.