Δ14CO2 observations are increasingly used to constrain recently added fossil fuel CO2 in the atmosphere. We use the LMDZ global atmospheric transport model to examine the pseudo-Lagrangian framework commonly used to determine recently added fossil fuel CO2 (CO2ff). Our results confirm that Δ14CO2 spatial variability in the Northern Hemisphere troposphere is dominated by the effect of CO2ff, whereas in the Southern Hemisphere, ocean CO2 exchange is more important. The model indicates that the free troposphere, at 3–5 km altitude, is a good choice for “background,” relative to which the recently added fossil fuel CO2 can be calculated, although spatial variability in free tropospheric Δ14CO2 contributes additional uncertainty to the CO2ff calculation. Comparison of model and observations suggests that care must be taken in using high-altitude mountain sites as a proxy for free tropospheric air, since these sites may be occasionally influenced by (polluted) boundary layer air, especially in summer. Other sources of CO2 which have Δ14C different than that of the atmosphere contribute a bias, which, over the Northern Hemisphere land, is mostly due to the terrestrial biosphere, whereas ocean CO2 exchange and nuclear industry and natural cosmogenic production of 14C contribute only weakly. The model indicates that neglecting this bias leads to a consistent underestimation of CO2ff, typically between 0.2 and 0.5ppm of CO2, with a maximum in summer. While our analysis focuses on fossil fuel CO2, our conclusions, particularly the choice of background site, can also be applied to other trace gases emitted at the surface.
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 A number of studies have taken advantage of this strong effect of fossil fuel CO2 emissions on Δ14C to constrain atmospheric mixing ratios of recently added CO2ff, demonstrating that Δ14C is likely to be the best method to independently and objectively verify fossil fuel CO2 emissions [Levin and Karstens, 2007; Levin et al., 2003; Turnbull et al., 2006; Hsueh et al., 2007; Meijer et al., 1996; Zondervan and Meijer, 1996]. These measurements have an immediate application to verify compliance with fossil fuel CO2 emissions targets such as the Kyoto Protocol [Riley et al., 2008; Levin and Rödenbeck, 2007]. The improved constraint on CO2ff mixing ratios is also useful for improving both bottom-up and top-down estimates of biospheric and ocean CO2 exchange. The reported CO2ff emissions have uncertainties of 5–20% at the national, annual scale [Gregg et al., 2008; Marland et al., 2006], and potentially much larger uncertainties at smaller spatial and temporal scales. Despite this, in a typical atmospheric CO2 inversion framework, where atmospheric CO2 mixing ratios are convolved with an atmospheric transport model to solve for the surface fluxes, the CO2ff flux is usually assumed to be perfectly known [e.g., Baker et al., 2006; Gurney et al., 2002] so that any bias in the estimates of CO2ff will contaminate estimates of the biospheric CO2 flux. Atmospheric observations can potentially reduce this problem, either by relating observed atmospheric Δ14CO2 values back to the CO2ff emission flux, or by “correcting” observed total CO2 mixing ratios for observed recently added CO2ff (derived from Δ14CO2). In this latter case, atmospheric observations directly constrain the recently added CO2ff mixing ratio in each sample, minimizing the need for emissions inventories or knowledge of wind patterns, and this methodology can be applied equally to small-scale studies such as flux tower measurements of CO2.
 To date, most researchers have used a straight forward approach to determining recently added CO2ff from Δ14CO2 observations, using a method based entirely on observations and independent of any explicit model [e.g., Palstra et al., 2008; Hsueh et al., 2007; Turnbull et al., 2006; Levin et al., 2003; Meijer et al., 1996]. In this pseudo-Lagrangian method, a parcel of air with an initial CO2 mixing ratio (CO2bg) and Δ14CO2 value (Δbg) moves across a polluted region, which modifies its CO2 mixing ratio and Δ14CO2 value to CO2obs and Δobs by the addition of CO2ff and any other sources or sinks of CO2 (CO2other), each with their own Δ14C value (Δff and Δother, the weighted mean Δ14C of the other CO2 sources), such that
Combining equations (1) and (2), Δff is known to be −1000‰ (the Δ14C value for zero 14C content), and if CO2obs, Δobs and Δbg are measured, CO2ff can be calculated as
where the second term is the bias (β) due to the effect of CO2other, such that
Δ14C is reported in per mil (‰) and (14C/C)abs the 14C:C ratio of the absolute radiocarbon dating standard (1.176 × 10−12 mol14C/molC; and is related to the commonly used primary measurement standard Oxalic Acid I [Karlen et al., 1968; Stuiver and Polach, 1977]). The (14C/C)samN is the 14C:C ratio in the sampled material, normalized to a δ13C value of −25‰. This normalization mathematically corrects for the effects of isotopic fractionation, such that processes which naturally fractionate during exchange (e.g., photosynthetic uptake of CO2) have no impact on atmospheric Δ14C, and thus only disequilibrium terms need to be considered.
 We note that the Δ14C of photosynthetic uptake (gross primary productivity) is implicitly assumed to be equal to Δbg. This is strictly true in the limit that the time (and space) between background and observation goes to zero. Some authors [e.g., Riley et al., 2008; Kuc et al., 2007] have instead assumed that Δ14C of photosynthesis is equal to Δobs, and in this case, equation (3) can be rewritten as
When integrated Δ14CO2 sampling is used, this formulation may be advantageous, as CO2obs is not required. In the case of flask sampling, CO2obs will usually be measured, so equation (3) is more convenient. If CO2other is zero, then equations (3) and (6) are exactly equivalent, but slight differences of up to 0.1 ppm in CO2ff can occur when both photosynthetic uptake of CO2 and the (Δobs − Δbg) difference are large. As this difference is much smaller than the other uncertainties discussed here, we will not discuss it further.
 Uncertainties in the CO2ff calculation method come primarily from statistical Δ14C measurement uncertainties, which are currently at best about 2‰ [Graven et al., 2007; Turnbull et al., 2007; Levin and Kromer, 1997], which translates to an uncertainty in CO2ff of 0.7 ppm for a single measurement. Additional uncertainty and potentially large biases come from the estimate of β and from the choice of Δbg. Note also, that when equation (6) is used, the choice of CO2bg will also play a role, and we will treat this in a future paper.
 For land regions, where most fossil fuel emissions occur, heterotrophic respiration, with it's potentially large 14C disequilibrium, is expected to be the main contributor to β. Some authors have assumed that β = 0 (i.e., all other sources have Δ14C equal to that of the background atmosphere and Δother = Δbg) [e.g., Levin et al., 2003], but others have estimated β values for heterotrophic respiration, such that if β is ignored, CO2ff would be consistently underestimated by up to 0.5 ppm in summer and 0.2 ppm in winter [Palstra et al., 2008; Riley et al., 2008; Hsueh et al., 2007; Turnbull et al., 2006].
 The pseudo-Lagrangian framework assumes that the upwind Δbg value can be measured, yet this is not possible or practical in most situations. For example, in the case of integrated samples collected over days to months (e.g., from plant material or integrated air sampling) the upwind region will likely have varied through the sampling period. Even for flask samples, the air parcel received at the observing site is a mixture of air received from a footprint region, rather than from a single point location. Thus we usually select samples collected at approximately the same time at a “clean air” background location to represent Δbg. The dearth of such measurements, and of continental surface locations sufficiently far from pollution sources, means that the high-altitude sites at Jungfraujoch, Switzerland (JFJ), and Niwot Ridge, Colorado, United States (NWR), have been most commonly used as European and North American background Δ14CO2 sites, respectively. Both sites are at ∼3500 m altitude. Schauinsland, Germany (SCH, 1205 masl [Levin and Kromer, 1997]) measurements have also been used for Δbg when other data has not been available [Kuc et al., 2007], although 2–3 ppm of CO2ff is regularly detectable in samples from this site relative to JFJ [Levin and Rödenbeck, 2007], thus biasing CO2ff estimates by the same amount. Figure 1 shows the location of these two sites, and others discussed in this paper.
 While the biases and uncertainties in the pseudo-Lagrangian calculation of CO2ff have been identified, they have not been quantitatively evaluated. Here we use the global atmospheric transport model LMDZ to simulate Δ14CO2 and these biases and uncertainties. In section 2, we describe the model and methods used to model Δ14CO2. We then demonstrate, in section 3.1, that our model reasonably simulates atmospheric Δ14CO2, and in section 3.2, that the surface spatial distribution of Δ14CO2 in the Northern Hemisphere is strongly dominated by the effect of fossil fuel CO2 emissions. In section 3.3, we examine how the choice of background site can influence the calculation of CO2ff, focusing on the choice of free tropospheric and high mountain sites as background. While we focus specifically on CO2ff, these results may also apply to other trace gas species which are emitted at the surface. In section 3.4, we examine the impact of systematic errors from other CO2 sources, notably the terrestrial biosphere, as represented by the second, bias term (β) in equation (1).
 We use the LMDZ4/INCA.2 global atmospheric transport model, described in detail by Hourdin et al.  and Hauglustaine et al. . The model resolution is 2.5° × 3.75°, with 19 vertical layers, including four layers in the first kilometer above the surface, a mean vertical resolution of about 2 km between 2 and 20 km, and four layers above 20 km. The model calculates its own meteorology, and the horizontal wind fields are then “nudged” every 6 h by the ECMWF reanalysis winds. The previous moist convection scheme has been replaced by a new implementation of Emanuel's [1991, 1993] moist convective mixing parameterization. Although LMDZ and INCA are coupled, chemistry is turned off in these simulations. The model has been validated for CO2 transport, and compared with the TransCom intercomparison results [Bousquet et al., 2008; Gurney et al., 2002]. LMDZ4/INCA.2 is on the low end of the TransCom model range for interhemispheric CO2 gradient and does not always capture a large enough vertical gradient in CO2 over the continents, apparently due to an overestimate in the modeled height of the planetary boundary layer. This type of problem is common to all the TransCom models, none of which obtain accurate CO2 vertical gradients at all locations in all seasons [Stephens et al., 2007]. This is the major weakness of the model for our application, and will result in smaller modeled surface horizontal gradients than expected, as well as an underestimate of vertical differences, particularly in the biases discussed in section 3.4. LMDZ4/INCA.2 does agree quite well with observations in the free troposphere. As with most large-scale models, LMDZ4/INCA.2 has difficulty simulating nighttime boundary layer CO2 values. Agreement between model and surface observations is better in summer than in winter, again likely related to the modeled boundary layer height. As with all global models of low resolution, it fails to adequately capture variability at some continental sites close to variables sources [Geels et al., 2007]. Despite these limitations, the model captures large-scale CO2 variability quite well, and falls within the range of TransCom models. This model version appears to be a significant improvement over the previous off-line version LMDZ3 [Bousquet et al., 2008]. Despite the known problems with modeled vertical transport, the CO2 mixing ratios at our sites are captured quite well in the model, and discussed in further detail in section 3.1.
 We transport fluxes of CO2 and 14CO2 separately in the model, and Δ14C is calculated from these offline, following equation (5). In the model, we implicitly include the normalization correction in the 14CO2 fluxes, except in the case of the fossil fuel CO2 flux, where we specify no isotopic information, since it contains no 14C. This means that we do not account for the 13C Suess effect, of 0.025‰ yr−1 (ftp://ftp.cmdl.noaa.gov/ccg/co2c13/GLOBALVIEW/), which would change Δ14CO2 by less than 0.04‰ yr−1. We do account for the change in 14CO2 mixing ratio due simply to the change in CO2 mixing ratio over time (e.g., biospheric uptake of CO2 removes CO2 seasonally, decreasing the 14CO2 mixing ratio, although it does not change Δ14CO2), calculating the effect of this at each model time step. The impact on Δ14C of each individual 14C source is estimated by calculating the Δ14CO2 value in the case where all other sources have Δ14C values the same as the atmosphere.
 We use CO2 and 14CO2 fluxes based on those described by Turnbull et al.  with some alterations, and also include a 14CO2 flux from the nuclear industry.
 The 14CO2 fluxes are from natural cosmogenic production, the nuclear industry (power generation and reprocessing plants), 14C ocean disequilibrium and heterotrophic respiration from the biosphere. We neglect the −0.1‰ yr−1 effect of radioactive decay of 14C in the atmosphere. Each 14CO2 global annual flux is rescaled to approximately match those calculated using the GRACE box model [Naegler and Levin, 2006] for our period of simulation 2002–2007. An initial uniform global background Δ14CO2 value was assigned in the model, and set such that the modeled absolute Δ14CO2 trend is in agreement with the observations at JFJ (see section 3.1). All fluxes are regridded to match LMDZ. The effect of each modeled 14C flux, as well as that of the 14C-free fossil fuel CO2 flux, on the mean global Δ14CO2 is shown in Table 1.
Table 1. Effect of Each Source on the Mean Global Atmosphere Δ14CO2a
In per mil per year. Calculated effect on mean global Δ14CO2 is based on an atmosphere with an initial Δ14CO2 value of 60‰ and 375 ppm of CO2. In the lowbio and highbio scenarios the ocean 14C flux is tuned to conserve the global trend.
 The 14CO2 terrestrial heterotrophic respiration term is first estimated using pulse-response functions from the CASA biosphere model for the year 2004 [Thompson and Randerson, 1999] and the time history of atmospheric Δ14CO2 [Levin and Kromer, 2004]. We then scale the resulting spatial and seasonal distribution to match the best estimate of the total 14CO2 flux predicted by the GRACE model for this time period [Naegler and Levin, 2006, 2009]. This is our standard (“standard”) case, with total annual impact of the biosphere on the atmosphere of 2.6‰ yr−1. In addition, we test the sensitivity of our results to uncertainty in this flux, using the lowest (“lowbio”) and highest (“highbio”) reasonable values as determined by the GRACE box model and atmospheric observations. We note that although fire CO2 emissions may have a much larger Δ14CO2 disequilibrium than heterotrophic respiration, due to the longer residence time of carbon in forests, fire CO2 flux is quite small. We calculate that the effect on global atmospheric Δ14CO2 of the 0.2 GtC yr−1 global fire CO2 flux [Balshi et al., 2007] with a fire return frequency of 200 years in boreal forests (i.e., Δ14C of −24‰) is about 0.02‰ yr−1. Hence, we fold this flux into the heterotrophic respiration flux.
 The gross ocean-to-atmosphere 14CO2 flux was first estimated using climatological surface ocean pCO2 [Takahashi et al., 2002], an assembly of surface ocean Δ14C of dissolved inorganic carbon (DIC) measurements from the GLODAP project (cdiac.ornl.gov/oceans/glodap/Glodap_home.htm), and the gas transfer formulation of Wanninkhof . Since the GLODAP data set is based on measurements from the 1970s and 1990s, we expect that the 14CO2 flux into the ocean is now much lower than this estimate. To account for this, we scale the spatial and seasonal distribution downward to match our annual total flux estimates (Table 1). Since this flux has very little impact on the Northern Hemisphere spatial distribution of Δ14CO2, in our lowbio and highbio cases, we scale the ocean flux to maintain the observed trend in Δ14CO2, but retaining the seasonal and spatial patterns.
 Cosmogenic production of 350 mol 14C/yr occurs throughout the atmosphere, with maximum production at the magnetic poles and a minimum at the equator. We distribute the 14CO2 production horizontally following Masarik and Beer , with the production rate (per mole of air) increasing linearly from zero at five kilometers to a maximum at the top of the model stratosphere. Figure 2 shows that our modeled vertical profile of Δ14C agrees fairly well with the very few stratospheric Δ14CO2 observations made in recent years [Nakamura et al., 1994, 1992]. Although this vertical distribution weights the 14CO2 production to somewhat higher altitudes than theory suggests [Masarik and Beer, 1999; Lal, 1988], when we applied a vertical distribution with more production close to the surface, our model did not build up enough 14C in the stratosphere (Figure 2). We further discuss the impact of the vertical distribution of this flux on our results in section 3.3.
 An estimation of the small 14C production flux from the nuclear industry is also included in the model. Both 14CH4 and 14CO2 are emitted by the nuclear power industry, with estimates of the total global production ranging from 45 to 85 mol 14C/yr in 2000 [UNSCEAR, 2000]. Differing from the GRACE box model result, we use a low estimate of the total annual, global production of 45 mol 14C yr−1, and distribute it evenly across the 30°N–60°N landmasses. Our total flux is likely too low, especially since nuclear power generation is increasing by about 3% per year, but we use this low value to account, in a simplistic way, for two things. First, many operable nuclear reactors are pressurized water reactors [International Atomic Energy Agency (IAEA), 2004], which emit 14CH4, rather than 14CO2 [UNSCEAR, 2000]. The long atmospheric lifetime of CH4 means that these emissions, while contributing to the overall trend in 14CO2, are unlikely to contribute a strong signal in 14CO2 at the surface. Since we do not model 14CH4 oxidation, our low flux estimate is designed to account for this issue. Second, while it is known that the emission rate of 14C varies with the type of reactor [UNSCEAR, 2000], it is not clear how much variability there might be between reactors of a single type, and whether the emissions are constant through time, or occur as discrete, large pulses of 14C. In the absence of better data, we do not attempt to distribute the emissions by point source, instead, we use a lower total emissions estimate, distributed evenly across the midlatitudes, noting that close to nuclear 14C sources, substantially larger emissions will occur, which are not accounted for in our model.
 The model is initiated with evenly distributed Δ14CO2, with the initial value set to obtain the best match with the annual mean JFJ values. The choice of site for tuning of the initial value is somewhat arbitrary, but comparison with the other sites (section 3) demonstrates that it is a reasonable choice. After a 2 year “spin-up” to remove the effect of the initial condition of Δ14CO2, we obtained model results for 2002–2007, and we extract the monthly mean values. We do not consider a longer time series, because we are specifically interested in examining the recent time period when fossil fuel emissions dominate the Δ14CO2 variability. During this time period, when the biosphere and ocean 14C disequilibriums with the atmosphere are reasonably small (because the bomb 14C is now quite well distributed throughout the reservoirs), we can consider them to be constant.
 When comparing our modeled results with mountaintop sampling sites, the mismatch between the modeled and real-world surface topography needs to be taken into account [Law et al., 2008; Geels et al., 2007]. While NWR and JFJ are both situated at 3500 masl, the modeled surface altitude of the grid box is 1600 m for NWR, and 500 m JFJ. To select the most appropriate model level at each site, we use the method described by Taylor , whereby observations of both the CO2 mixing ratio seasonal cycle phase and its amplitude are compared with those at each model level, following
E is the root mean square error; σobs and σmdl are the standard deviations of the detrended seasonal cycle for the observations and model level. R is the correlation coefficient of the fit between the observed and model level values. The standard deviations capture the difference in the seasonal amplitude, and R captures the difference in the seasonal cycle phase. The best model level is determined as that where E is minimized; that is, the differences in phase and amplitude between observations and model are smallest. We select model level 2 (450 m above model ground) SCH, and model level 4 (1500 m above model ground) for JFJ (Figure 3). At NWR, E has the same minimum value for levels 2 and 3; we select level 2, as the phase agreement is slightly better, but this indicates that the choice of model level is not critical. In all cases, the selected model level is above the model surface, but below the true sampling site altitude, consistent with expectations. The agreement between the selected model level and the observed CO2 seasonal cycle phase is good for all sites. There is a slight underestimate in the seasonal amplitude at JFJ and SCH, likely because the model biosphere flux values we used have slightly too small a magnitude, whereas the phase in this flux may be more reliable [Gurney et al., 2004]. Again, we note that LMDZ, along with other global transport models, has some difficulty in obtaining the correct magnitude of vertical gradients over the continental land. Because we are selecting for the model level that best matches the observations, our method actually reduces the impact of this problem. We also tested for the impact of choosing an adjacent model level where the fit is slightly poorer but still reasonable, and for averaging two adjacent model levels; this did not significantly impact our interpretations.
3. Results and Discussion
3.1. Comparison of Modeled and Observed Δ14CO2
 The modeled Δ14CO2 values at three sites where observations are available for most of our modeled time period (Niwot Ridge, Colorado, United States, Jungfraujoch, Switzerland, and Schauinsland, Germany) are compared with the observations in Figure 4. As described in section 2, the model was tuned such that the modeled absolute Δ14CO2 trend is in agreement with the observations at JFJ. This results in good agreement between model and observations at the other sites. The larger scatter in observations at NWR may be due to the difference in sampling method: at JFJ and SCH, the observations are integrated monthly mean values [Levin et al., 2008], whereas at NWR, measurements were taken from weekly flask samples [Turnbull et al., 2007]. The overall downward trend agrees well with the observations at all sites, decreasing by 5‰/yr, an unsurprising result since we tuned the flux fields to obtain the observed trend. The difference between the sites is well captured, and the seasonal cycle also appears reasonable. At these mountain sites, the impact of possible biases in modeled vertical transport (described in section 2) is small, because they lie mostly in the free troposphere. This suggests that our model fluxes are realistic, and allows us to use the model to further examine Δ14CO2 as a proxy for fossil fuel CO2 concentration deviation from background (see equation (3)).
3.2. Spatial Distribution of Δ14CO2
 The mean LMDZ modeled surface Δ14CO2 values for 2002–2007 are shown in Figure 5. Figure 5 shows the lowest model level, representing the surface; this is comparable in both pattern and magnitude of the spatial distribution to the next model level up (∼180 m above model surface). In the Southern Hemisphere, the spatial variability is quite weak, but dominated by the effect of ocean disequilibrium. In the Northern Hemisphere, Δ14CO2 variability is strongly dominated by the effect of (14C-free) fossil fuel emissions, with the lowest values in regions where fossil fuel emissions occur, and gradual increases in the Δ14CO2 values downwind from the source regions. This strong relationship can be clearly seen by comparison with Figure 5 (bottom), which shows the spatial variability in Δ14CO2 due only to fossil fuel emissions (i.e., when all other CO2 sources have Δ14C values equal to that of the atmosphere). Not only the spatial pattern, but also the magnitude of the Δ14CO2 differences in the Northern Hemisphere, are comparable between the two modeled distributions shown in Figure 5. As discussed earlier, the choice of model level can have substantial impact on the Δ14CO2 values for mountain sites, where the model resolution is unable to capture the topography correctly. For the global distribution, this impacts only a few discrete locations.
 The spatial distribution is in general agreement with Δ14CO2 observations over Northern Hemisphere land, capturing the broad continental variability in the observations (Figure 6). The large-scale model is unable to adequately resolve fine structure, such as the very low Δ14C values observed close to large cities (e.g., in California, and also in comparison to fine-scale Δ14CO2 distributions obtained from wine ethanol in Europe [Palstra et al., 2008]). The model does not always capture the magnitude of the spatial variability particularly well, and this is likely related to the known biases in the modeled vertical transport [Turnbull et al., 2009]. However, our results are similar to other model predictions for the 1990s and 2000s [Hsueh et al., 2007; Randerson et al., 2002].
3.3. Choice of Background Site
 CO2ff in equation (3) is the fossil fuel CO2 added relative to a background site, and the choice of background site thus strongly influences the calculated CO2ff. In today's atmosphere (with ∼380 ppm of CO2 and Δbg of ∼60‰), a +1‰ bias in Δbg will result in an overestimate in CO2ff of +0.3 ppm. This is the same change in CO2ff as caused by an equal, opposite change in Δobs of −1‰.
 Since it is difficult to identify surface sites which are not influenced by local sources, most researchers have assumed that free tropospheric observations, and high mountain sites as a proxy for the free troposphere, represent a reasonable background relative to which the recently added fossil fuel CO2 in boundary layer air can be determined. We use the model to test how well these locations represent “background.”
 First, we consider the best choice of altitude for free troposphere “background” sites. Cosmogenic production of 14CO2 results in a vertical change in Δ14CO2, with increasing values in the upper atmosphere, especially in the stratosphere (Figure 2), and a background site too high in the troposphere might be influenced by this effect. Figure 7 shows the modeled Northern Hemisphere mean vertical distribution of Δ14CO2 from the surface to 10 km altitude, if CO2ff emissions are excluded from the model. The vertical change is less than 1‰, with negative values (relative to the surface) in the lower troposphere, due to the influence of surface fluxes of biospheric respiration and nuclear industry 14CO2. Above about 7 km, however, the Δ14CO2 values begin to increase, due to the cosmogenic 14C flux, which strongly dominates in the stratosphere (see Figure 2). This does not change substantially if the cosmogenic production is weighted closer to the surface (Figure 7). Therefore, we recommend that altitudes below 6 km be used for the background site, to avoid any possibility of bias from cosmogenic production. To also avoid influence from the planetary boundary layer, free tropospheric sites above about 3 km should be used. We select ∼3.5 km altitude because most aircraft sampling programs are able to routinely collect samples at this altitude, and this is the approximate altitude of several existing high mountain sampling sites.
 The Northern Hemisphere free troposphere is relatively well mixed with respect to Δ14CO2 (Figure 8), with variability across the midlatitudes of about 3‰ (noting the exception over Central Asia where the high mean surface altitude influences the 3.5 km level), an order of magnitude smaller than the surface spatial variability of 38‰. Although this variability will be difficult to distinguish with current measurement uncertainties, it immediately indicates that care should be taken in the choice of background site, since it may bias CO2ff.
 To more closely examine the choice of free tropospheric background over Northern Hemisphere land, we use model results from two example sites. These are selected to represent “typical” sampling locations, where both biological CO2 emissions and fossil fuel CO2 emissions occur nearby, and regular aircraft sampling of boundary layer and free tropospheric air already occurs (only model data is shown here). Our sites are: Cape May, New Jersey, UNITED STATES (CMA, 38.83°N, 74.31°W), on the North American eastern seaboard; and Orleans, France (ORL, 48.83°N, 2.5°E), just south of Paris (Figure 1). Figure 9 (middle) shows the modeled Δ14CO2 differences between the surface site of interest and the free troposphere at 3.5 km above the site due to all sources other than CO2ff. Small wintertime biases from cosmogenic production and nuclear industry sources, roughly cancel one another out, and are apparently due to the strong continental boundary layer buildup in winter. As noted earlier, the nuclear industry 14C flux is uncertain and poorly represented in the model. Since the source is either very local (14CO2 emissions from the power plant point sources) or very dispersed throughout the atmosphere (oxidation of 14CH4 emissions), in fact, its effect may be smaller at most sites, even if we underestimated the total emissions. The dominant effect is from the biosphere, for which the source is roughly colocated with the fossil fuel emissions we are interested in. The effect is strongest in summer, when respiration is high, and much weaker in winter. When any free troposphere site is used as background, this biospheric contribution cannot be avoided, and instead, we use a model to estimate and correct for it in the second term in equation (3). This is discussed in detail in section 3.4.
 High-altitude mountain sites have been assumed to represent free tropospheric air, and are most commonly used to determine Δbg [e.g., Palstra et al., 2008; Hsueh et al., 2007; Kuc et al., 2007; Levin et al., 2008]. Mountain sites do not, however, provide a perfect proxy for the free troposphere background, since they may be influenced more quickly by vertical mixing from the local surface than is the case for the same altitude in the free troposphere over a low-altitude surface. Using the LMDZ simulation, we test how well the NWR and JFJ sites represent free tropospheric air over our “typical” sites in North America and Europe. Comparison of the modeled NWR Δ14CO2 with the 3.5 km level over the eastern United States shows that NWR is typically 1–2‰ lower than the eastern U.S. free troposphere, and in winter, and exhibits a much stronger seasonal cycle (Figure 4). A similar pattern is seen when JFJ is compared with the western European free troposphere. In both cases, the modeled difference is almost entirely due to fossil fuel CO2 emissions, indicating that both of these mountain sites are slightly influenced by local fossil fuel emissions. The simulated bias depends on the model level chosen to represent these sites, and the magnitude of the biases would differ by ∼1‰ if a different model level was selected (see section 2). Nevertheless, the model result indicates that mountain sites are not a perfect proxy for free tropospheric air.
 The observational records from NWR and JFJ suggest that there may also be substantial local surface influence during summer which is not seen by our large-scale model, likely due to sub-grid-scale vertical mixing events not captured at our model resolution. This is clear in the comparison of the model with the observed NWR values. The model agrees quite well with the “cleaned” data set (solid symbols in Figure 4), but does not reproduce the low values associated with local pollution events (open symbols in Figure 4) when air from the nearby Denver metropolitan region is lofted to the NWR site, and identified by elevated carbon monoxide mixing ratios [Turnbull et al., 2007]. Including these locally polluted samples in the calculated monthly mean depresses the springtime monthly mean NWR values by 2 to 4 ‰, changing interannually depending on the frequency and strength of these local pollution events. The much longer JFJ record (started in 1986 [Levin et al., 2008]) shows similar fluctuations in the magnitude of the spring decrease in Δ14CO2. Since these samples are collected as integrated biweekly or monthly means, it is not possible to positively identify local pollution events in the Δ14CO2 record, but local pollution events bringing air from the (populated) valley below can be seen in other proxies [Lugauer et al., 2000, 1998]. This supports the possibility that interannual variability in the strength of springtime drawdown in Δ14CO2 at JFJ may be related to the frequency and strength of such local pollution events.
 We also note that incursions of stratospheric air, which is enriched in 14C, could cause similar, but opposite biases from time to time at these high-altitude sites. For example, during synoptic dry intrusions, stratospheric air can be delivered even to surface sites, but is not likely to be well captured by large-scale models [Stohl, 2001].
 It is apparent that when remote and/or high-altitude sites are used to represent the background, care should be taken to ensure that seasonal transport effects such as those described above are identified and/or avoided. We suggest that conditional integrated sampling, which samples the air only during periods identified as from a clean air sector, or alternatively, flask sampling, where individual polluted samples can be positively identified, provide the best likelihood of obtaining the most representative “background” air.
 The modeled differences of 1–3‰ due to the choice of background site are similar to or smaller than current measurement uncertainties, but they will result in biases, rather than random variability. Since equation (3) calculates recently added fossil fuel CO2, as the CO2ff overburden relative to the background used, the choice of background site is critical to the interpretation of the results. This does not preclude the use of remote or mountain sites as background, and indeed these sites will likely continue to provide the best available estimates of background Δ14CO2 values for the Northern Hemisphere.
 We do suggest, however, that in light of the differences between background sites, and particularly the apparent seasonality of the differences between sites, care should be taken in selection of the appropriate background site for a particular experiment. Any remaining biases must be corrected for in the bias term β. Low-altitude coastal sites or midcontinent sites far from pollution sources could also be used as background. It is, however, difficult to identify sites of these types which are not influenced by local sources. Conditional sampling only when meteorological conditions indicate air from a clean air sector could alleviate this problem. When CO2ff at multiple surface locations is being compared, it may be most appropriate to select the “cleanest” of these sites as local background, rather than using a regional background site. In this case, any bias in the choice of background will be the same for all sites, allowing direct comparison between the various sites, but any seasonal or interannual bias in the chosen local background site would need to be carefully evaluated. Ultimately, methods of determining CO2ff which are less reliant on the underlying Lagrangian assumption will be needed.
3.4. Effect of Other Fluxes (and Their Uncertainties) on Fossil Fuel CO2 Calculation
 In our model, where the contributions of each 14C source are quantified individually, we can determine the bias (β, second term in equation (1)) in the calculation of CO2ff due to other sources of 14C, which cannot be removed by judicious choice of background site. We calculate the effect of β on the determination of CO2ff in boundary layer air, using free tropospheric air at 3.5 km above each site as the background, and the same example sites we discussed in section 3.3.
 We calculate CO2ff when β is calculated from the model, and when β is neglected (Figure 9). The seasonal cycle in CO2ff that arises is dominated by seasonal differences in atmospheric transport, and only weakly from the seasonality in the CO2ff flux itself. For example, the modeled CO2ff values at CMA are very similar when the CO2ff flux is input into the model with no seasonality (Figure 10). When we separate the CO2ff flux into CO2ff fluxes from each continent (Europe-CO2ff, North America-CO2ff, etc, data not shown), we find that the majority of the seasonality in CO2ff comes from the local continent, indicating that most of the seasonality at the surface comes from seasonal differences in venting of the boundary layer, with stronger venting in the summer reducing the surface CO2ff mixing ratio. Only weak contributions to the surface seasonal cycle come from seasonally varying cross-tropopause exchange and free tropospheric transport.
 The effect of fossil fuel CO2 dominates the calculation of CO2ff, and β contributes only 10% of the signal in summer, and less than 2% in winter at these sites. The bias is driven by the gross biospheric 14C flux, and we see no significant bias from the cosmogenic 14C production flux, or from the oceans, even at Northern Hemisphere coastal sites. The model indicates a small bias from the nuclear industry, but even doubling of this flux would have only a minor effect. Our model evenly distributed the nuclear industry flux, and so does not capture the possibility of significant biases close to power plants, such as those observed and corrected for by Levin et al.  and Palstra et al. .
 In our standard scenario, at midlatitude Northern Hemisphere sites, the terrestrial biosphere contributes a positive bias of 0.5 ppm in summer, but less than 0.2 ppm in winter (Figure 9). This seasonal difference is due to the strong seasonality of biospheric respiration, which is largest in the summer months, and the magnitude of the bias is similar throughout the midlatitude Northern Hemisphere. Our sensitivity tests indicate that the highbio estimate of the biosphere flux would cause a consistent, positive summertime bias in CO2ff of 0.8 ppm, with a much smaller bias of 0.3 ppm in winter (Figure 9, bottom). The lowbio scenario produces a bias of less than 0.4 ppm in summer and 0.2 ppm in winter. The apparent underestimate of vertical gradients in LMDZ will result in an underestimate of the fossil fuel CO2 gradient and of the bias in our analysis; the magnitude of this problem is not well quantified, but is likely similar to, or smaller than the effect of the range of biosphere flux estimates we use. Thus a range of values for the bias is 0.4–0.8 ppm in summer, and 0.2–0.3 ppm in winter at these sites.
 This bias is quite consistent across most of the Northern Hemisphere land (Figure 11), except for higher values in the southeastern United States. Although we are able to estimate and correct for this bias using the model results, CO2ff calculations will be less reliable when the bias term is large relative to CO2ff. For example, Δ14CO2 observations likely cannot be reliably used to determine fossil fuel CO2 emissions in most of the Southern Hemisphere, where the ocean bias has similar magnitude to CO2ff. Similarly, the tropics have lower CO2ff emissions and high bias, due to the strong biospheric exchange there.
 Our model studies indicate that Δ14CO2 does indeed provide a good tracer for recently added fossil fuel CO2. CO2ff accounts for almost all of the Northern Hemisphere Δ14CO2 spatial variability, with only small contributions from other sources.
 When calculating the recently added fossil fuel CO2 mixing ratio using Δ14CO2, uncertainty is contributed by uncertainty in the Δ14CO2 measurement, and from the choice of background site, and biases from other sources of 14C.
 The choice of background site is critical to interpretation of the amount of “recently added” fossil fuel CO2. Free tropospheric air appears to be a reasonable choice for background, if the biases, mainly from the terrestrial biosphere, are accounted for. Although high-altitude mountain sites currently provide the best estimates of clean background air, they may be influenced by local fossil fuel pollution, especially in summer. These differences are typically of the same magnitude as the current Δ14CO2 measurement uncertainties, but may result in a bias rather than random noise. Therefore care must be taken in choosing the most appropriate background for each experiment. The uncertainty due to the choice of background site depends on the experimental design, when using mountain sites for background, but is likely less than 2‰ or 0.7ppm in CO2ff.
 When the recently added fossil fuel CO2 contribution is calculated using the commonly used pseudo-Lagrangian method described here, relative to remote (marine boundary layer, high altitude or free tropospheric) background sites, a small bias due mostly to terrestrial biospheric 14C flux, is induced. In most temperate Northern Hemisphere regions, ignoring the bias would result in an underestimate of CO2ff of 0.5 ppm in CO2ff in summer, and 0.2 ppm in winter. Our model indicates that the maximum uncertainty in this bias is 0.3 ppm in summer and 0.1 ppm in winter. Some regions, notably the southeastern United States, have a higher bias in the summertime, and thus extra care must be taken in interpreting Δ14CO2 observations in this region.
 When these biases are accounted for, the total uncertainty in the calculation of CO2ff from Δ14CO2 measurements of 2‰ precision is less than 1 ppm for a single observation, including uncertainty from the Δ14CO2 measurement (0.7 ppm), uncertainty in the magnitude of the bias (0.3 ppm) and uncertainty in the choice of background site (0.7 ppm).
 Our results indicate that accurate estimates of the fossil fuel CO2 mixing ratio, with quantified uncertainties, can be obtained from atmospheric samples. The challenge remains to infer fossil fuel CO2 fluxes from this data. For small-scale studies, observationally obtained flux estimates from the radon method impart ∼30% additional uncertainty in local flux estimates [Levin et al., 1999] and plume measurements of city pollution combined with meteorological information obtain uncertainties in fluxes of ∼50% [Trainer et al., 1995]. For larger scales, atmospheric transport models are the most common approach. These models have significant errors with complex structure [Stephens et al., 2007; Gurney et al., 2002, 2004]. Interactions of seasonally varying biospheric fluxes and atmospheric transport contribute much of this uncertainty [Gurney et al., 2002, Figure 3] and this will play a much smaller role for fossil fuel fluxes. Furthermore, recent comparisons of modeled CO2 with observations [Law et al., 2008; Patra et al., 2008; Lauvaux et al., 2008] suggest considerable improvement. Transport model error will likely still dominate any inversion study of fossil fuel fluxes from Δ14CO2, but it seems unlikely to confound such an inversion. How much information the combined observation/modeling system will add to economically based inventories with their uncertainties of 5–20% [Marland et al., 2006] must await properly formulated observing system simulation experiments.
 This paper was improved by thoughtful comments and suggestions by two anonymous reviewers. The Niwot Ridge time series includes some additional data not previously published. Thanks go to Scott Lehman, Chad Wolak, and the NOAA/ESRL Carbon Cycle team for providing these measurements. Some stratospheric Δ14CO2 measurements were kindly provided by Takakiyo Nakazawa at Tohoku University.