Estimating discrimination against 13C during photosynthesis at landscape, regional, and biome scales is difficult because of large-scale variability in plant stress, vegetation composition, and photosynthetic pathway. Here we present estimates of 13C discrimination for northern biomes based on a biosphere-atmosphere model and on National Oceanic and Atmospheric Administration Climate Monitoring and Diagnostics Laboratory and Institute of Arctic and Alpine Research remote flask measurements. With our inversion approach, we solved for three ecophysiological parameters of the northern biosphere (13C discrimination, a net primary production light use efficiency, and a temperature sensitivity of heterotrophic respiration (a Q10 factor)) that provided a best fit between modeled and observed δ13C and CO2. In our analysis we attempted to explicitly correct for fossil fuel emissions, remote C4 ecosystem fluxes, ocean exchange, and isotopic disequilibria of terrestrial heterotrophic respiration caused by the Suess effect. We obtained a photosynthetic discrimination for arctic and boreal biomes between 19.0 and 19.6‰. Our inversion analysis suggests that Q10 and light use efficiency values that minimize the cost function covary. The optimal light use efficiency was 0.47 gC MJ−1 photosynthetically active radiation, and the optimal Q10 value was 1.52. Fossil fuel and ocean exchange contributed proportionally more to month-to-month changes in the atmospheric growth rate of δ13C and CO2 during winter months, suggesting that remote atmospheric observations during the summer may yield more precise estimates of the isotopic composition of the biosphere.
 Two primary approaches for estimating ecosystem-scale ΔA13 are (1) the extrapolation of isotopic measurements of plant and soil organic matter and (2) the analysis of the isotopic composition of CO2 in air that is varying from biosphere-atmosphere gas exchange [Keeling, 1958, 1961]. In principal, the two approaches should yield equivalent estimates of ΔA13 (from mass conservation), yet in practice, the two approaches frequently diverge. The ΔA13 inferred from air sampling is sensitive to environmental conditions over a period of days to weeks [Bowling et al., 2002; Ekblad and Hogberg, 2001], whereas plant and soil organic matter often reflect environmental conditions over periods of months to years [Buchmann et al., 1998].
 Isotopic measurements of plant and soil organic matter (δ13Cb) can be converted into photosynthetic discrimination (ΔA13) by removing an offset imposed by the atmosphere at the time of fixation (δ13Catm) [Farquhar et al., 1989]:
This approach also requires the critical assumption that discrimination in downstream processes such as construction, maintenance respiration, and decomposition is minimal or that discrimination and carbon fluxes associated with these processes can be explicitly accounted for [Buchmann et al., 1998]. The challenge with implementing this approach at the biome scale comes from the wide variability of isotopic composition observed both between species and within individual plants [Benner et al., 1987; Korner et al., 1991; Hayes, 1993]. Sources of variation include species-to-species differences in photosynthetic pathway (i.e., C3 versus C4), discrimination in the biochemical formation of different plant compounds (i.e., lignin versus cellulose), leaf architecture (i.e., needles versus broad leaves), and environmental stress. In addition, use of equation (1) requires knowledge of the isotopic composition of the local atmosphere at the time of CO2 fixation (δ13Catm). This quantity is difficult to estimate because of diurnal and seasonal variability in the δ13C of canopy and planetary boundary layer air [Lloyd et al., 1996] and because of long-term changes in the isotopic composition of the global atmosphere (the 13C Suess effect) [Keeling et al., 1979]. Despite these limitations, plant functional types show consistent offsets in δ13Cb that may serve as a basis for regional scale extrapolation of ΔA13 [Flanagan et al., 1996; Brooks et al., 1997].
 Isotopic measurements of soil organic matter (SOM) have the advantage of integrating belowground net primary production (NPP) over a number of disturbance cycles [Bird et al., 1996; Tieszen et al., 1997]. However, spatial variability of soil 13C within an ecosystem can be quite large [Bird and Pousai, 1997]. In addition, the relatively large mean residence time of bulk SOM leaves open the possibility that small levels of discrimination associated with decomposition, dissolved organic carbon leaching, or microbial C fixation could induce an offset over a number of years between the isotopic composition of SOM and soil CO2 fluxes [Ehleringer et al., 2000].
 The other widely used approach for estimating ecosystem-level ΔA13 was developed by Keeling [1958, 1961]. With this approach, the isotopic composition of the source (δ13Cb) can be estimated from the intercept of a linear regression between measured atmospheric δ13C (at time t and height z) and the reciprocal of the concentration CO2 (t, z):
where M is also obtained from the regression and represents the product of the background CO2 concentration and the difference between the isotopic composition of δ13Cb and the isotopic composition of the background air. Once δ13Cb is known, ΔA13 can be estimated by removing the mean isotopic composition of the atmosphere at the time of fixation (δ13Catm) using equation (1). However, as with the plant and soil isotope sampling approach, it is difficult to quantify δ13Catm, because it requires knowledge of the distribution of ages of CO2 emitted as ecosystem respiration (and the concurrent time history of δ13C in the local atmosphere). The Keeling plot approach combines the discrimination of various elements within an ecosystem (and between various ecosystems within a region) in proportion to their contribution to the total biosphere-atmosphere CO2 flux.
 Use of equation (2) requires the assumption of mixing between an atmospheric reservoir with a uniform composition and an isotopically homogeneous source or sink. At many scales of interest, however, this assumption does not always apply, even over the course of a single set of flask measurements. At the ecosystem scale, autotrophic and heterotrophic respirations may have different isotopic signatures. If these components contribute differentially during the course of a measurement, the regression intercept will be difficult to interpret. Other approaches, including relaxed eddy accumulation [Bowling et al., 1999], the use of additional isotopic constraints (δ18O) [Yakir and Wang, 1996], and canopy-planetary boundary layer (canopy-PBL) models [Lloyd et al., 1996], may be used to isolate multiple isotopic sources.
 Here we estimate the isotopic composition of net seasonal CO2 exchange (δ13Cn) at high northern latitudes by analyzing National Oceanic and Atmospheric Administration Climate Monitoring and Diagnostics Laboratory (NOAA/CMDL) and Institute of Arctic and Alpine Research (INSTAAR) flask measurements north of 50°N from 1993 to 1996. As defined here, δ13Cn includes fossil fuel, ocean, and remote C4 ecosystem components in addition to seasonal exchange from terrestrial ecosystems. We estimate and remove minor contributions to δ13Cn from ocean, fossil fuel, and remote C4 ecosystem fluxes, using an atmospheric model and prescribed surface fluxes. With a coupled biosphere-atmosphere model that includes time delays for heterotrophic respiration, we then solve for the optimal combination of three biosphere parameters, ΔA13, NPP light use efficiency (ε), and a Q10 factor (a temperature sensitivity parameter for respiration that is defined in section 2.5) that provide a best fit with the NOAA/CMDL and INSTAAR CO2 and δ13C data. We define ΔA13 as a flux-weighted photosynthetic discrimination, integrated over the entire growing season, for northern biomes including boreal forest and arctic tundra. Our analysis builds upon previous work by Knorr and Heimann , where optimal NPP and Q10 values were estimated by using biosphere and atmosphere models and seasonal CO2 observations, and is comparable in approach with Kaminski et al. .
 There are several advantages to initially focusing our analysis on high northern latitudes. First, while understanding the contribution of C4 photosynthesis to global NPP is an essential prerequisite to partitioning ocean and land carbon sinks using atmospheric 13CO2 [Fung et al., 1997; Lloyd and Farquhar, 1994; Still et al., 2002], it is also important to characterize spatial and temporal variation in discrimination by C3 vegetation. While there are several C4 species present in boreal forest biomes, their abundance (and thus their contribution to NPP and net ecosystem production (NEP)) is small [Schwarz and Redmann, 1988; Collatz et al., 1998], allowing us to isolate the isotopic composition of the C3 end-member. Second, as compared with midlatitude, tropical, and Southern Hemisphere regions, in the far north the terrestrial biosphere is the dominant contributor to seasonal variation in CO2; fossil fuel and ocean contributions to seasonal variation are minor [Heimann et al., 1998; Randerson et al., 1997]. The large seasonal amplitudes of both CO2 and δ13C in the north facilitate removal of the long-term secular trend caused primarily by fossil fuels and allow for relatively low levels of uncertainty in retrieval of ecophysiological parameters.
2.1. Atmospheric Data Selection and Trend Removal
 We used monthly mean data (available at http://www.cmdl.noaa.gov/ccg/) from all available NOAA/CMDL and INSTAAR remote flask stations north of 50°N (Table 1) [Trolier et al., 1996]. These northern stations are influenced mostly by arctic and boreal biomes on seasonal timescales [Kaminski et al., 1996]. We only included data points in our analysis when monthly mean CO2 and δ13C were simultaneously available.
Table 1. NOAA/CDML and INSTAAR Flask Measurements Used in This Study
CO2 Seasonal Amplitude ppm
δ13C Seasonal Amplitude, ‰
Alert, Northwest Territories
Mould Bay, Northwest Territories
Point Barrow, Alaska
Ocean Station “M”
Cold Bay, Alaska
Mace Head, County Galway
 A smoothing spline was used to remove the low-frequency secular trend at each station [Enting, 1987]. After the secular trend was removed, we truncated each time series at the beginning and end by 7 months to remove any edge effects induced from the spline. A single mean value for each station, obtained from the average of the low-frequency spline fit, was added back to each point in the time series for use with equation (2). We restricted our analysis of the detrended time series to the period between January 1993 and December 1996. We chose this 4-year period because most stations were sampled during this time, allowing a retrieval of biosphere parameters that was not strongly biased by variations in station density.
2.2. The Isotopic Composition of Net Seasonal CO2 Exchange
 With the detrended monthly station data, we estimated the isotopic composition of net seasonal CO2 exchange, δ13Cn, using equation (2) (Table 2). We accomplished this using a type II regression program that accounted for errors associated with both the CO2 and δ13C measurements and that provided standard error estimates for both the slope and intercept regression parameters [Press et al., 1992]. This regression approach generally gives more negative δ13Cn intercepts than type I regressions where the independent variable is assumed to have no error [Sokal and Rohlf, 1980].
Table 2. Isotopic Composition of Net Seasonal CO2 Exchange (δ13Cn) From 1993 to 1996
All Year (January–December)
All stations combined
 At each station, we estimated δ13Cn (1) using all available data (January–December), and we also estimated separately for (2) summer (May–September) and (3) winter (October–April) periods (Table 2). In the regression procedure each monthly data point was assigned a standard error of 0.2 ppm for CO2 and 0.05‰ for δ13C to approximately capture the atmospheric variation in weekly flask measurements that contribute to the filtered monthly mean [Trolier et al., 1996]. We estimated δ13Cn for the combination of all stations by pooling all of the detrended station data together in the regression analysis.
2.3. Construction of a Multistation Time Series North of 50°N
 We made a combined time series for all of the stations north of 50°N from January 1993 to December 1996 by averaging all available station data at each monthly time interval described in section 2.1. Since not all of the stations were active during each time interval, the number of stations used to construct the combined time series varied between 6 and 10. We did not perform any interpolation to account for missing data at individual stations. In the averaging process each station was weighted equally. Overall, the records from individual stations were mostly complete during the 1993–1996 period. In sum, 425 monthly mean data values were used to construct this combined time series (a perfect record without any missing monthly mean data would have contained 480 points for the 4-year interval). Standard deviation estimates for the combined time series reflected station to station differences in CO2 and δ13C.
2.4. Atmosphere Model Description
 Pulse-response (or Green's) functions of the Goddard Institute for Space Studies (GISS) tracer model were used to construct a simple representation of a mean atmosphere with 16 “basis” surface regions (eight land and eight ocean) and a monthly time step (Table 3). The GISS tracer model uses 4-hour winds and monthly convection statistics from the GISS general circulation model and operates with a 1-hour time step [Fung et al., 1991]. The pulse response functions were generated by evenly distributing a 1-Pg C source at the surface in each basis region for each month of the year and then recording the resulting three-dimensional (3-D) distribution (8° × 10° × 9 vertical layers) of CO2 over a period of 3 years. On land the monthly pulse sources were distributed spatially within each basis region according to the annual mean distribution of NPP derived from the Carnegie-Ames-Stanford approach (CASA) model [Randerson et al., 1997]. Ocean pulse sources were distributed evenly over the area of each ocean basis region (Table 3). Fossil fuel emissions were estimated using a single separate basis region with a spatial distribution described in section 2.8.
Table 3. Atmospheric Basis Regions
North America (high latitudes)
north of 56°N
Eurasia (high latitudes)
north of 56°N
North America (midlatitudes)
North America (low latitudes)
Eurasia (low latitudes)
Subtropics and tropics (Northern Hemisphere)
Southern Hemisphere land
North Atlantic (high latitudes)
north of 40°N
North of Pacific (high latitudes)
north of 40°N
North Atlantic (low latitudes)
North Pacific (low latitudes)
south of 48°S
 In each land basis region a terrestrial biosphere model (described in section 2.5) was used to estimate 13C and 12C fluxes for each monthly time step. The terrestrial biosphere and atmospheric models were fully coupled in that surface fluxes from one land basis region in one time step would influence the isotopic composition of the atmosphere and consequently would influence the magnitude of isotopic exchange in terrestrial basis regions in future time steps. Because the coupling occurred at a monthly time step and terrestrial ecosystem isotope uptake occurred relative to the isotopic composition of the atmosphere at month t − 1, it is likely that the model somewhat underestimated the effects of seasonal changes in atmospheric δ13C on the isotopic composition of ecosystem biomass and fluxes. In contrast to the terrestrial biosphere-atmosphere coupling, ocean and fossil fuel isotope fluxes were prescribed for the duration of each atmospheric model run using data sources described below.
 Within each land basis region the terrestrial biosphere model was 1-D; its input data and output fluxes did not vary spatially. Driver data (e.g., temperature or absorbed photosynthetically active radiation (APAR)) for the terrestrial model consisted of a single average value for each basis region, obtained by averaging data products with a higher spatial resolution. At each time step, atmospheric CO2 concentrations resulting from terrestrial biosphere, ocean, and fossil fuel fluxes were added together using the appropriate pulse response functions for each. The procedure for estimating the atmospheric distribution of δ13C was similar, as described below.
 In each pulse model simulation we carried two tracers, total carbon from the surface flux and the product of total carbon and the δ13C isotopic signature of this flux in δ notation, i.e., C × δ13C. The distribution of δ13C in the atmosphere was then obtained by dividing the atmosphere distribution of δ13CO2 × CO2 by the atmosphere distribution of CO2 at the end of the simulation.
2.5. Terrestrial Biosphere Model Description
 We separately estimated monthly NPP and heterotrophic respiration (Rh) at each time step (t) and in each of the eight terrestrial basis regions (x). Monthly NPP was estimated as the product of APAR (in units of megajoules) and a light use efficiency (ε; in units of g C MJ−1 PAR) [Montieth, 1972]:
APAR in equation (3) was estimated for each basis region by taking the average of 1° × 1° monthly maps generated by the CASA model. The CASA APAR estimates were derived from satellite-derived estimates of normalized difference vegetation index and total solar insolation [Bishop and Rossow, 1991; Sellers et al., 1994; Randerson et al., 1997]. The light use efficiency (ε) was uniform across all basis regions and time steps and, as described in section 2.9, is one of three “free” parameters solved for by comparison with atmospheric data.
 The heterotrophic respiration model had two components, a seasonal distribution and a time lag associated with the allocation of NPP to wood, fine roots, and leaves and then the decomposition of coarse woody debris, fine root litter, leaf litter, and fast and slow soil organic matter components (Figure 1). The seasonal distribution of Rh had a Q10 temperature dependence
where k(i) is the decomposition rate constant for each pool i, C is the temporally and spatially (from basis region to basis region) varying carbon content of each pool, and Q10 represents the nonlinear factor that relates Rh to mean monthly air temperature, T. Mean monthly air temperatures for each basis region, x, were constructed from the spatial average of a 0.5° × 0.5° monthly climatology [Leemans and Cramer, 1990]. For our initial focus on high northern latitude ecosystems, we did not explicitly include soil moisture limitation on NPP or Rh.
 NEP is approximated in our model each month as the difference between NPP and Rh (Figure 2).
We make the additional approximation that this flux is entirely in the form of biosphere-atmosphere CO2 exchange. While a formal definition of NEP includes any lateral, river, or biosphere-atmosphere flux of C that influences the net carbon balance of an ecosystem, our analysis focused on seasonal timescales, and so this approximation is probably valid. It is worth noting, however, that fires are indistinguishable from Rh in our model formulation, and so they will impact on our inversion estimates of the Q10 temperature sensitivity and ΔA13, since they are a nonnegligible part of high-latitude seasonal CO2 exchange [French et al., 2000].
 Because of persistent fossil fuel CO2 release of 13C-depleted carbon, respiration of the terrestrial biosphere is not in equilibrium with the δ13C content of the contemporary atmosphere (the δ13C Suess effect [Keeling et al., 1979]). The magnitude of the isotopic disequilibria depends on the residence time of C in vegetation, litter, and soils: The larger the mean residence time, the greater the isotopic disequilibria. Since the relative amounts of Rh and NPP in NEP vary from month to month, disequilibria effects have the potential to influence the isotopic composition of source estimated by equation (2). We accounted for disequilibria effects in each biosphere-atmosphere simulation by allowing the biosphere model to reach steady state with the atmosphere in the year 1750. Then, from 1750 to 1993 we used ice core and atmospheric δ13C measurements from Francey et al.  to adjust the 13C of NPP and thus the 13C content of model carbon pools. We tested our assumptions about the turnover time of carbon in the terrestrial biosphere with a sensitivity analysis described in section 2.9.
 We implicitly assumed that plant respiration was instantaneous (had a residence time that was less than the model time step of 1 month) and that there was no 13C discrimination associated with this process. Because we attempted to separate and correct for isotopic disequilibria caused by time delays in Rh, our estimates of ΔA13 represent a canopy-level discrimination associated with net photosynthetic assimilation [Lloyd and Farquhar, 1994]. It is not an ecosystem-level discrimination (ΔE13) that would include components from ecosystem respiration (as defined by Buchmann et al. ).
2.6. Ocean Exchange
 Ocean exchange and its isotopic composition was estimated for each ocean basis region at each time step by separately considering the one-way gross fluxes:
Equations (6a) and (6b) determine the flux of 13C from the atmosphere to the ocean (ao) and from the ocean to the atmosphere (oa). The 13C flux is determined by the total one-way flux, F, the 13C/12C ratio of the donor reservoir, R, and the fractionation factor associated with the flux, α. Fao and Foa were calculated from
 The 13C/12C ratio of the atmosphere, Ra, and pCO2atm were estimated for the 1993–1996 period from the average of the atmospheric measurements listed in Table 1. For the ocean 13C/12C ratio, Ro, we used measurements of δ13C in dissolved inorganic carbon (DIC) sampled from 1980 to 1995 as presented by Gruber et al. . The data were averaged over time and were linearly extrapolated to latitudinal bands in each ocean basin. The isotopic fractionation factors captured differences between DIC and gaseous CO2 isotopic composition [Zhang et al., 1995]. The temperature dependence of the fractionation factors [Zhang et al., 1995] was calculated using monthly averaged simulated sea surface temperature from the National Center for Atmospheric Research Community Climate System Ocean Model [Doney et al., 2001].
2.7. C4 Vegetation
 We determined the contribution of C4 vegetation to the NPP flux in each land basis region using a new global map of C3 and C4 fractions [Still et al., 2002]. The map was produced by combining physiological modeling and remote sensing products. The C4 component of NPP in each basis region (Table 4) was assigned a discrimination value of 4.4‰. We solved for the discrimination of the remaining C3 component of NPP (ΔA13) in the inversion analysis described in section 2.9.
Table 4. Absorbed Photosynthetically Active Radiation and C3 and C4 Percent Net Primary Production
APAR, MJ PAR m−2yr−1
North America north of 56°N
Eurasia north of 56°N
North America 40°N–56°N
North America 24°N–40°N
All land 0°N–24°N
All land 0°S–56°S
2.8. Fossil Fuels
 We generated fossil fuel pulse functions using the GISS atmosphere model with a 1-Pg C source distributed spatially according to 1990 fossil fuel emissions [Andres et al., 1996]. As with the terrestrial and ocean pulse functions, we constructed a separate pulse function for each month. However, in contrast to the ocean and terrestrial pulse functions, for fossil fuels we considered only a single spatial region, with the spatial distribution of fluxes prescribed by Andres et al. . For each year from 1990 to 1997, annual totals from Marland et al.  were used to adjust the fossil pulse response functions to account for interannual variation. Seasonal variation in emissions was modeled using a sine wave with a peak in January, a minimum in July, and a peak-to-trough amplitude of 30%, consistent with the seasonal distribution of consumption in North America and Europe [Rotty, 1987] (Figure 2). This probably had the effect of overestimating the seasonality of fossil fuel emissions in the tropics. However, fossil fuel emissions in the tropics are relatively small [Andres et al., 1996]. Given that the focus of our study is on high northern latitudes and that detailed spatial data on seasonal emissions are sparse, it is difficult to justify a more elaborate representation of fossil emissions.
 To estimate the isotopic variations in Northern Hemisphere fossil fuel, we assumed that gas, solid, and liquid components of fossil fuel emissions were 20, 45, and 35%, respectively, based on 1990 data from North America, Western Europe, Germany, Centrally Planned Europe, Centrally Planned Asia, and Far East Asia [Marland et al., 2000]. Gas, solid, and liquid fuels were assigned isotopic values of −42, −24, and −28‰, respectively [Andres et al., 2000]. We used compiled, available records for the United States [Rotty, 1987] to describe seasonal variation in gas, solid, and liquid fuel use. The dominant contributor to seasonal variation in fossil fuel emissions was natural gas. Natural gas consumption in the United States doubled during winter months because of increased heating demands (from 6.4% in July to 13.3% in January) [Rotty, 1987].
2.9. Biosphere-Atmosphere Model Simulation
 The primary objective of the model simulations was to estimate the combination of ΔA13, ε, and Q10 parameters that best described the high-latitude NOAA/INSTAAR observations. We accomplished this sequentially with two steps. First, we solved for the combination of ε and Q10 that minimized the error between modeled and measured monthly CO2 as described by the following cost function:
where Cobs was the combined and detrended monthly time series of NOAA CO2 described in section 2.3 (the average of the stations in Table 1 for each of the 48 monthly intervals between January 1993 and December 1996), Cmod was the combined and detrended CO2 time series from the atmospheric model (consisting of the average of the surface grid cells containing the stations listed in Table 1), and σobs(j) was the standard deviation of the observations across all available stations in each time step. Each estimate of Cmod included prescribed ocean and fossil fuel emissions as described in sections 2.6 and 2.8. We estimated Θ1 for a series of terrestrial biosphere model scenarios (section 2.5) in which ε ranged between 0.1 and 0.9 g C MJ−1 PAR (at 0.01 g C MJ−1 PAR increments) and the Q10 simultaneously ranged between 1.0 and 2.2 (at 0.01 increments). Thus Θ1 was computed for ∼9600 terrestrial biosphere model scenarios. We report minimum values of ε and Q10 in section 3 along with the shape of the cost function. With the first step of this minimization process we were effectively searching for two free variables (ε and Q10), using a constraint of 48 mean monthly CO2 observations from high northern latitude stations (section 2.3).
 Second, with the ε and Q10 that minimized equation (8), in a second series of model runs we varied ΔA13 between 15 and 23‰ at 0.01‰ increments. The cost function for this second minimization step had the same form as equation (8), but for δ13C instead of CO2. With the second step of this minimization process we were effectively searching for one free variable (ΔA13) using a constraint of 48 mean monthly δ13C observations from high northern latitude stations (section 2.3).
 We also used the monthly atmospheric distribution of δ13C and CO2 from each model run to calculate the modeled source composition, δ13Cn (model), from equation (2). The combined model time series was constructed in an identical manner to the combined NOAA/INSTAAR time series, described in section 2.1 and 2.3, by averaging the δ13C and CO2 of surface grid cells that corresponded to the stations listed in Table 1. The ΔA13 of the terrestrial biosphere that minimized the difference between observed and modeled δ13Cn served as a second cost function, Θ2.
Equation (9) serves as a useful alternate to equation (8) because it emphasizes different aspects of the NOAA and INSTAAR data record. Specifically, equation (9) (which is based on the modeled and observed intercepts from equation (2)) is relatively insensitive to biases in the shape of the modeled seasonal cycle that are present in both δ13C and CO2. Specifically, equation (9) depends more on the relationship between δ13C and CO2 (the slope and intercept in δ13C and CO2 phase space) than on the exact shape of the δ13C seasonal cycle.
 We also used our atmospheric pulse model to estimate the atmospheric isotopic composition at the time of photosynthetic fixation (δ13Catm). We estimated (δ13Catm) by weighting monthly surface-level atmospheric δ13C values over the continents north of 40°N (over basis regions 1, 2, 3, and 4 in Table 3) by monthly APAR from the same regions (described in section 2.5).
 In the following results section, we separately provide the distribution of the error function for the two steps in our inversion procedure. Formal estimates of the errors are difficult to retrieve because of bias introduced from the use of modeled atmospheric winds.
 In a series of sensitivity tests, we report the optimal ΔA13 of the terrestrial biosphere (minimum of equation (9)) when ocean, fossil fuel, and remote C4 fluxes were sequentially removed from the model calculation of CO2 and δ13C. We also conducted sensitivity analyses in which the mean residence time of each pool in the terrestrial biosphere model (shown in Figure 1) was divided by a factor of 2.
3.1. The Isotopic Composition of Net Seasonal CO2 Exchange
 Using all available mean monthly data north of 50°N from January 1993 through December 1996, we find that the isotopic composition of net seasonal CO2 exchange, δ13Cn, was −26.7‰ ± 0.2‰ (Table 2). The δ13Cn varied between winter and summer: wintertime flask data (October–April) yielded a δ13Cn of −26.3‰ ± 0.4‰, while summertime flask data (May–September) yielded a δ13Cn of −27.1 ± 0.3‰ (Table 2).
 Monthly and seasonal anomalies in CO2 and δ13C from the stations in Table 1 were coherent across widely distributed and remote northern observation sites (Figure 3). May, June, and July of 1995 had anomalously low CO2 and anomalously high δ13C. In contrast, during the growing season in 1996, CO2 was anomalously high, and δ13C was anomalously low (Figure 3c). The CO2 and δ13C anomalies had a highly significant negative Pearson correlation (r = −0.84, df = 46, and p < 0.01). A linear regression of the anomalies in δ13C and CO2 (equation (2)) yielded a source isotopic composition of −22.9‰ ± 4.6‰. The anomalies may reflect, in part, interannual changes in ΔA13. The relatively low isotopic source value of the CO2 anomalies (−22.9‰), however, may also reflect a nonnegligible contribution to interannual variability from high-latitude air-sea gas exchange, biomass burning, or changes in the isotopic composition of fossil emissions.
3.2. Biosphere-Atmosphere Model Results
 The ε and Q10 values that simultaneously minimized error between modeled and NOAA/CMDL CO2 observations were 0.47 g C MJ−1 PAR and 1.52 (Table 5). The optimized ε value generated a mean North American NPP of 217 g C m−2 yr−1 north of 56°N, a mean Eurasian NPP of 271 g C m−2 yr−1 north of 56°N, and a global total of 55 Pg C yr−1. The optimized Q10 value generated a mean residence of terrestrial carbon of 42 years for North American and Eurasian regions north of 56°N (basis regions 1 and 2), a mean residence time for tropical and subtropical regions of the Northern Hemisphere of 18 years (basis region 7), and a global mean residence time of 24 years (given the structure of the biosphere model described in the text and in Figure 1).
Table 5. Sensitivity Analysis of ϵ Q10, and ΔA13 Retrievalsa
Fluxes Included in Simulation
ϵ, gC MJ−1 PAR
MRT Regions 1 and 2, years
MRT Region 7, years
Global NPP, Pg C/yr
δ13C Global Disequilibria, Pg C ‰/yr
For each of the four sensitivity model runs (runs 2–5) the surface fluxes used in the inversion analysis were modified either by removing the fossil fuel (FF) source, removing the ocean source, removing the influence of C4 vegetation, or modifying carbon pools within the terrestrial biosphere model. The ΔA13 values are reported using equation (9) for the minimization function.
Mean residence time (MRT) of all terrestrial biosphere model carbon pools were decreased by a factor of 2 from those shown in Figure 1. This had the effect of changing the isotopic disequilibria and the isotopic composition of heterotrophic respiration.
 These results demonstrate that the Q10 function also partially constrains the latitudinal distribution of ecosystem carbon turnover times and thus constrains the latitude distribution of the isotopic disequilibria of Rh, a critical parameter in regional and global scale double deconvolution estimates of ocean and land carbon sinks [Ciais et al., 1995]. With an optimized Q10 of 1.52, the global isotopic disequilibria forcing at the start of our simulations in 1990 was 22.7 Pg C ‰ yr−1.
 More generally, the combinations of ε and Q10 that minimized error (equation (8)) were correlated because these two parameters together determined the seasonal distribution of the net land flux (Figure 4). The ε sets the magnitude of NPP, since the distribution of APAR was fixed from satellite observations (section 2.5). The Q10 set the seasonal distribution of Rh based on monthly air temperatures (equation (4)). In northern biomes a higher Q10 leads to a higher fraction of Rh emitted during summer months than during winter months. For the ecosystem to sustain a net carbon sink during the summer (required to match the observations in Figure 3a), ε must also be high, so that NPP exceeds Rh [Lloyd and Taylor, 1994].
 The value of ΔA13 that minimized the difference in the observed and modeled source composition was 19.4‰ (equation (8) and Figure 5). Use of an alternate cost function led to an ΔA13 estimate of 19.0‰ (equation (9)).
 From our sensitivity analysis, retrieval of ΔA13 from atmospheric data appeared most sensitive to fossil fuel emissions. Excluding fossil fuel fluxes from the analysis led to an increase in ΔA13 by 0.2‰, while excluding ocean exchange led to a decrease of ΔA13 by 0.1‰ (Table 5). Excluding remote C4 ecosystems also caused a decrease of ΔA13 (oceans and C4 fluxes have a similar impact on ΔA13), but for the northern regions that were the focus of this analysis, the effect was <0.05‰. Cutting the turnover time of each terrestrial biosphere model carbon pool in half caused the isotopic disequilibria forcing to decrease by ∼7 Pg C‰ yr−1 and caused ΔA13 to increase by 0.1‰.
 With the ΔA13, ε, and Q10 values that minimized the cost functions, the model does a fair job at reproducing the mean seasonal cycle at high northern latitude observation stations, although during the early part of the growing season the model drawdown of CO2 occurs earlier than in the observations (Figure 6). Over the continents the seasonal cycle of δ13Catm is even greater than at the observation stations (Figure 6c). For example, over land north of 56°N, δ13Catm increases by ∼1.0‰ from May to September. Over land between 40°N and 56°N, δ13Catm increases by ∼0.8‰ from May to September. For grid cells in the middle of the continents, this seasonal variation is even larger (data not shown). When monthly δ13Catm values over continental regions north of 40°N were averaged over the growing season (weighted according to monthly APAR), we obtained a value of −8.0‰.
4.1. ΔA13 for Northern Biomes
 Two lines of evidence suggest that ΔA13 for northern biomes, integrated over the growing season, is between 19.0 and 19.6‰. The first is the analysis of high northern latitude CMDL and INSTAAR data that documents a more negative source during summer months (−27.1‰) than during winter months (−26.3‰). During the summer, fluxes from ocean and fossil fuels are small relative to fluxes from the terrestrial biosphere (Figure 2). To a first approximation, during summer months it may be possible to ignore monthly variations arising from fossil fuel and ocean exchange, whereas during the winter this would be impossible. With a mean summer source composition of −27.1 ± 0.3‰ and an APAR-weighted atmospheric composition over northern continents of −8.0‰ from 1993 to 1996 (section 2.9), it is possible to directly estimate a value of ΔA13 at ∼19.6‰ without use of an atmospheric inversion.
 Can fossil fuel emissions be neglected during summer? In this context, it is crucial to note that only the seasonally varying component of fossil fuel emissions induces a bias in a direct estimate of ΔA13. The seasonally invariant component of the fossil fuel flux (which constitutes most of the fossil flux; see Figure 2) is mostly removed from the NOAA and INSTAAR data prior to our analysis by the application of the low-frequency smoothing spline (section 2.1). For the same reason, only the seasonally varying component of the ocean exchange would induce a bias. More generally, with any analysis of regional aircraft or surface measurements the distinction between background and seasonally varying contaminants must be addressed prior to correcting for their effects with a mixing model approach. This is particularly challenging when CO is used to correct for fossil fuel contamination; only the seasonally varying component of CO is appropriate for fossil fuel corrections on seasonal timescales, and variation arising from reaction with atmospheric OH or biomass burning sources must be separately accounted for [Bakwin et al., 1998].
 The second line of evidence for ΔA13 being ≥19.0‰ comes from our full biosphere-atmosphere inversion analysis that includes seasonal variation in atmospheric transport, and it accounts for the seasonal distribution of fossil fuel, ocean, and remote C4 ecosystem contributions. Given that the minima of two cost functions differ by ∼0.4‰ (minima of 19.4 and 19.0‰ for equations (8) and (9), respectively), that the standard error of the observed δ13Cn is at least 0.2‰ (Table 2), and that the range from sensitivity analysis is 0.3‰ (Table 3), it is difficult to ascribe a confidence level to ΔA13 of less than ±1.0‰. Precise estimates of uncertainty are limited with the inversion techniques because of the difficulty in quantifying biases introduced from atmospheric transport. Nevertheless, the sharp increase in the cost functions below 18.0‰ and above 21.0‰ and our sensitivity analysis allow us to effectively bracket the high-latitude flux-weighted value. Our ΔA13 estimate is slightly less than the mean of respiration estimates from boreal ecosystems in central Canada [Flanagan et al., 1996] and is comparable with estimates inferred directly from high northern latitude aircraft observations in the lower [Nakazawa et al., 1997] and upper troposphere [Zahn et al., 2000].
 Other atmospheric models may generate stronger land/ocean CO2 gradients during the growing season. If the atmosphere was more enriched over land during summer months than we were able to produce with our monthly pulse model (Figure 6), ΔA13 may be even larger than our inversion model suggests. Also, with our atmospheric pulse model we were unable to capture any covariance between diurnal variations in the atmospheric isotopic composition over land and diurnal patterns of CO2 fixation. Failing to capture this covariance may impose an offset in our inversion estimates of ΔA13 to the extent that fixation occurs at times when CO2 in the boundary layer deviates significantly from background troposphere concentrations. Failing to capture this diurnal process would most likely cause us to underestimate ΔA13 in our inversion.
 Boreal forest and arctic tundra biomes are the greatest contributors to seasonal variation in CO2 at the stations listed in Table 1 [Kaminski et al., 1996; Randerson et al., 1997], and so the ΔA13 estimate we obtain from our inversion mostly reflects a flux-weighted average of C3 vegetation in these two biomes. Since fluxes from nonvascular plants such as mosses and lichens have a significant role in modulating atmospheric CO2 in the far north on seasonal timescales, these fluxes also contribute to our estimate of ΔA13. Mosses may account for 10–40% of boreal forest and wetland NPP [Frolking, 1997; Szumigalski and Bayley, 1996] and have an isotopic composition that often is depleted by several per mil as compared with conifer trees growing at the same sites [Brooks et al., 1997; Flanagan et al., 1997]. Some of this depletion is caused by elevated levels of atmospheric CO2, near the forest floor, from soil respiration.
 The contribution of fluxes from mosses and lichens at high northern latitudes makes it difficult to compare our biome-level inversion estimates with models that focus exclusively on vascular plants with stomatal regulation [Lloyd and Farquhar, 1994]. Similarly, the dominance of conifers in many regions makes it difficult to directly compare our estimates with syntheses that focus solely on herbaceous plants [Korner et al., 1991].
 The top-down inversion estimate of ΔA13 presented here may allow us to place a constraint on the relative contribution of various plant functional types to the total seasonal CO2 exchange at high northern latitudes. Evergreen conifers tend to have lower ΔA13 values (∼18.5 ± 1.0‰) than deciduous (larch) conifers (∼19.5 ± 1.0‰) [Kloeppel et al., 1998], while deciduous trees, shrubs, and mosses appear to have ΔA13 values that frequently exceed 20‰ (∼21–23‰) [Brooks et al., 1997; Flanagan et al., 1997]. Consequently, our biome-level estimate of 19.0–19.6‰ suggests that deciduous trees, shrubs, and mosses have an important but limited role in shaping the total seasonal flux in northern biomes.
 Several previous analyses of ΔA13 at the ecosystem scale have assumed that δ13Catm was constant over the duration of the growing season. We find that δ13Catm increases by up to 1.0‰ from May to September over northern land regions. This offset has implications for ecosystem-level ΔA13 analyses in that different species/plant functional types may take up carbon over different periods within the growing season. This seasonal trend in δ13Catm is consistent with observations from central Canada [Flanagan et al., 1997] and is larger than the seasonality observed at remote, marine NOAA/CMDL and INSTAAR flask observation stations that are frequently invoked as a reference for ecosystem-level studies.
4.2. Light Use Efficiency
 Three kinds of approaches exist for estimating ε at regional and biome scales, two that depend on NPP measurements and a third that depends on an atmospheric inversion of the net flux (this study, Kaminski et al. , and Knorr and Heimann ). The NPP-based methods can be categorized as those that extrapolate in situ ε observations using vegetation or biome type [Heimann et al., 1989; Ruimy et al., 1994] and those that use a dynamic model of ε that responds to variation in climate [Running and Hunt, 1993; Runyon and Waring, 1994; Field et al., 1995]. Development and application of the NPP-based methods requires, as a minimum, precise NPP observations at a series of sites that span the observed range of environmental variability.
 The top-down atmospheric inversion approach for estimating ε is complementary to the NPP-based methods in that NPP observations are not required. The tradeoff is that additional constraints must come from models of Rh, APAR, and atmospheric transport and from very precise atmospheric trace gas measurements. On seasonal timescales in middle- and high-latitude regions of the Northern Hemisphere, these constraints are relatively well defined. Heterotrophic respiration is highly sensitive to temperature, and a number of studies have defined the form of this relationship [Lloyd and Taylor, 1994; Raich and Potter, 1995]. In the tropics, additional challenges arise in applying the inversion approach from relatively small CO2 gradients (from rapid tropical convective mixing), greater contribution of ocean exchange, uncertainties in our understanding of the relationship between soil moisture limitation, respiration, and NEP, and differing light use efficiencies of C4 plants.
 Given the limitations of the inversion approach described above, our estimate of a NPP-based ε of 0.47 gC MJ−1 PAR for boreal and arctic biomes is greater than observations from boreal and temperate evergreen conifer forests (∼0.3 gC MJ−1 PAR) but less than or comparable with boreal deciduous (aspen) and temperate deciduous (mixed hardwood) observations (∼0.5 gC MJ−1 PAR) [Gower et al., 1999]. Since the cost function does not rise sharply when ε and Q10 values covary, it is possible to match the observed values of ε in boreal conifers by accepting a series of slightly less ideal solutions with smaller Q10 values (Figure 4). Biases in our estimates of ε may also arise from any systematic offset in our satellite-derived APAR estimates (presented in Table 4).
 Compared with dynamic ε models, the inversion value we obtain is ∼20% greater than the CASA globally maximum ε value (0.39 gC MJ−1 PAR) that was obtained from a set of worldwide NPP measurements [Field et al., 1995]. Part of this difference may be attributed to a greater fraction of diffuse light at high northern latitudes, which would increase an atmospheric inversion-based estimate of ε as compared to the CASA analysis that relied on global NPP observations, and did not involve a partitioning of PAR into diffuse or direct components.
 In principal, the inversion approach presented here could be extended to estimate gross primary product based light use efficiencies. A model of plant maintenance and growth respiration would be required, along with a model that described the age distribution of plant respiration. Including plant respiration would probably require a biosphere-atmosphere model that operated with a shorter time step.
4.3. Use of the Q10 Function in Biogeochemical Models
 We used mean monthly temperature data to obtain a Q10 of 1.52. This Q10 value is appropriate for use with ecosystem NPP models that operate with a monthly time step, predict respiration fluxes using air temperature, and are used to predict seasonal to interannual dynamics in heterotrophic respiration.
 Our biome-level estimate falls in the middle of a 1.4–1.6 range of Q10 values reported from a metaanalysis of soil respiration data that were analyzed with respect to mean monthly air temperatures [Raich and Potter, 1995] and is consistent with other atmospheric inversions that relate respiration fluxes to monthly air temperatures [Kaminski et al., 2002; Knorr and Heimann, 1995]. Together, the atmospheric inversion results and the soil respiration syntheses challenge the idea that a single canonical Q10 value of 2 is appropriate for relating ecosystem responses to temperature and reinforce the idea that Q10 values must be specifically defined for a given time and space scale of temperature variability.
 The top-down estimate of the Q10 is much lower than estimates obtained from the comparison of soil respiration fluxes with soil temperatures (median Q10 of 2.4 [Raich and Schlesinger, 1992]). The reason for this stems from physical, physiological, and ecological limits on scaling respiration estimates. If we had used soil temperatures instead of air temperatures to drive our respiration model, the Q10 value that minimized the error function would have increased for any given value of ε, because soil temperatures have a damped seasonal cycle as compared with air temperatures [Ryan, 1991].
 Another critical factor that must be accounted for in the Q10 formulation is that the pool of metabolically active carbon in plant biomass and soil changes seasonally because of increases in living plant biomass over the growing season and, in the far north, because of soil thaw and an extension of the active layer through the summer and into the fall. This process is only partially captured with our model formulation; biomass pools do change seasonally, but soil depth does not. In addition, fires in the boreal forest contribute to some of the interannual variability in atmospheric CO2 shown in Figure 3 [French et al., 2000]. In our analysis, we do not explicitly correct for the fire fluxes (which occur exclusively during summer months), and so we may overestimate the sensitivity of heterotrophic respiration to temperature.
4.4. Improving Future Estimates of ΔA13
 Knowledge of the magnitude and isotopic composition of monthly fossil fuel emissions limits our ability to retrieve more precise estimates of ΔA13 in northern ecosystems using the inverse atmospheric approach. In our sensitivity analysis, removal of the fossil fuel source led to the largest perturbation of our ΔA13 estimate (0.2‰; see Table 5). In the far north it is not clear if fossil emissions increase or decrease during the summer; there is greater demand for heating during winter months, yet there is greater economic activity during the summer. With the development and application of higher resolution atmospheric models the impact of fossil fuels on inversion results is likely to be even greater, particularly for continental regions like the United States that have high fossil emissions. Natural gas is a primary source of this limitation, because its isotopic composition varies widely and its use may vary substantially from summer to winter and also, possibly, from year to year. More detailed information on monthly fossil fuel emissions is also essential for inversion analyses that retrieve seasonally varying sources and sinks of CO2, particularly with the double deconvolution approach [Ciais et al., 1995], but also for the case of time-dependent CO2 inversions [Rayner et al., 1999].
 Here we provide top-down estimates of three ecophysiological parameters for northern tundra and boreal forest biomes. We find that ΔA13 is ∼19.0–19.6‰, ε is ∼0.47 gC MJ−1 PAR, and the Q10 is ∼1.52. On land these three ecophysiological parameters may be among the easiest to retrieve from remote atmospheric observations. Ultimately, developing top-down estimates of biospheric parameters provides additional dimensions (beyond flux estimates) to test our understanding of ecosystem function across multiple time and space scales. For example, changes in disturbance regime in the boreal forest will alter fluxes, but it will also alter ΔA13 in a way that is predictable and is possibly detectable over a period of several decades.
 With longer time series of precise CO2 and δ13C measurements, it may be possible to identify seasonal variation in ΔA13 and magnitude of ecosystem isotopic disequilibria, taking advantage of the subtle month-to-month variations in δ13C-CO2 phase space. In principle, it should also be possible to solve for discrimination from all land and ocean regions, following the time-dependent methodology developed by Rayner et al.  and Bousquet et al.  for atmosphere CO2. If land and ocean fluxes at the same latitude are truly distinguishable with surface flask data, then a δ13C inversion should yield ocean and land discrimination values that are consistent with direct observation.
 J. T. R. gratefully acknowledges support from a NASA IDS grant NASA/MDAR NAG5-9462 and a DOE Alexander Hollaender Distinguished Postdoctoral Fellowship.