The TAC tall tower measurement site was set up in 2012 as part of the UK DECC (Deriving Emissions linked to Climate Change) network (Fig. 1). It is operated by Bristol University and the University of East Anglia. More details on the site and the network have been previously published (Stanley et al., 2018). The site is located in Norfolk, approximately 140 km north-east of London. It was thought to be the most appropriate site in the UK DECC tall tower network for characterizing ffCO2 emissions from the UK using 14CO2 because it has the most influence from fossil fuel sources and the least influence from nuclear power stations. The TAC tower site has three inlet heights: 54, 100, and 185 m. CO is observed from the 100 m inlet once every 20 min. The CO2 observations are reported as 1 min means and all heights were sampled at an interval of 20 min per height. The highest height (185 m) was used for the 14CO2 measurements as it was assumed that it would be the most representative for well-integrated air masses. A background observation is necessary for the 14CO2 method to evaluate the relative depletion caused by recently added emissions of ffCO2. Different types of sites have been utilized as background in previous studies: relatively unpolluted sites upwind of significant fossil fuel CO2 sources (Lopez et al., 2013), high-altitude observations (Bozhinova et al., 2014; Levin and Kromer, 1997), free troposphere observations from an aircraft (Miller et al., 2012; Turnbull et al., 2011), and a mildly polluted site upwind of the polluted site (Turnbull et al., 2015). MHD, located on the west coast of Ireland, was used as the background site for this study and weekly sampling was performed when air masses were representative of clean air coming from the Atlantic (Fig. 1). This study utilized both flask and, for some species, high-frequency in situ data from two sites (MHD and TAC), Table 1 gives an overview of the measurement techniques used, the calibration scales, and the operator of the specific instrument or method. For CO, the flask and the in situ data were reported on different calibration scales. Comparisons of co-located observations at MHD show that there is a significant difference between the two scales (Fig. S1 in the Supplement). Conversion between the CSIRO-98 and the WMO-2014 CO scale is non-trivial as there is a time and concentration dependent difference between the two scales and no published conversion method is yet available. It was decided that only the in situ data would be utilized for the CO ratio analysis to avoid any effect these calibration scale differences might have on the CO ratio analysis. At TAC, the in situ CO observations (100 m) were made at a different height to the flask sampling (185 m). Observations of CH4 and CO2 at the two heights were similar (less than 0.4 % difference) within the same hour the flasks were taken, indicating that it was acceptable to use the CO observations at 100 m. A comparison of the concentration of CH4 and CO2 in the flask samples vs. the respective time-matched in situ observations at 185 m showed good agreement (less than 0.2 % difference). The measurements are reported as dry air mole fractions in ppm (µmol mol-1) and ppb (nmol mol-1).

The sampling procedure was based on the method used by the National Oceanic and Atmospheric Administration Carbon Cycle Greenhouse Gases (NOAA CCGG; Lehman et al., 2013). At MHD, the sampling of an additional flask for 14CO2 analysis was added to the existing weekly NOAA CCGG flask sampling collection. A manual instantaneous sampling module was constructed for TAC, using a KNF pump to pressurize and a Stirling cooler (Shinyei MA-SCUCO8) set to 0 ∘C to dry the sample. Additionally, a 7 µm particle filter was added to avoid contamination of the sampling module, and a check valve in addition to a toggle valve were added to ensure that existing measurements at the site were not influenced. A selection of tests, including a side-by-side comparison with the NOAA CCGG sampling unit at MHD, was performed before deployment to TAC. At TAC, samples were collected weekly into 2 L glass flasks (NORMAG, Germany, based on the NOAA CCGG design).

Mole fractions were simulated at each measurement site using the Lagrangian particle dispersion model NAME (Numerical Atmospheric dispersion Modelling Environment) developed by the UK Met Office (Jones et al., 2007). Hypothetical particles are released into the model atmosphere at a rate of 10 000 per hour at the location of the observation site and transported backward in time for 30 d. It is assumed that when a particle resides in the lowest 0–40 m of the model atmosphere, pollution from ground-based emission sources is added to the air parcel (Arnold et al., 2018; Manning et al., 2011). The particle residence times in this surface layer are integrated over the 30 d simulation to calculate a “footprint” of each measurement that quantifies the sensitivity of the observation to a grid surrounding the measurement site (Manning et al., 2011). These footprints can be multiplied by flux fields to simulate the mole fraction due to each source at each instant in time. An example of such a footprint, also called back trajectory, can be found in the Supplement (Fig. S2). In a similar fashion the NAME model can be run forward in time to simulate the concentration of a substance in the modelling domain. To simulate the concentration of a substance in the modelling domain, theoretical particles are released at the emission source location (point sources and area sources) with a rate that is relative to the emission source strength. We separate the CO2 mole fraction into a background concentration CO2,bg and a contribution from each source i: 1CO2=CO2,bg+∑iCO2,i. The background concentration can be determined by applying statistical methods to high-frequency observations (Barlow et al., 2015; Ruckstuhl et al., 2012) or estimated by models (Balzani Lööv et al., 2008; Lunt et al., 2016). In this work, high-frequency data existed only for 12CO2 but not its isotopes and there was no model-derived background available for the isotopes; therefore, MHD data were used as background for the simulation of all CO2 isotopes. While 13CO2 and 14CO2 measurements at MHD were selectively sampled during clean air conditions (high wind speeds from the Atlantic Ocean), the high-frequency 12CO2 data also contained pollution events. To exclude the pollution events, a rolling 15th percentile value (±20 d) was calculated and used as 12CO2 background. The 15th percentile of the MHD data was chosen for the background curve over other percentiles because it successfully removed short-term concentration changes and pollution events. In addition to creating a smooth curve, the 15th percentile of the MHD data also fitted low concentrations observed in TAC, outside of the growing seasons (not much CO2 uptake due to photosynthesis), well. Similarly, for the 13CO2 and 14CO2 background, rolling median values (±30 d) were calculated. These rolling median values created a smoother seasonal cycle compared to using the closest observed value.

This section describes the method and the equations used to model 12CO2, 13CO2, and 14CO2 at TAC. The modelling of the two stable CO2 isotopes was necessary in order to be able to simulate the 14CO2. A framework to simulate 14CO2 was developed as a tool to investigate the observations and possible constraints of the radiocarbon method. A basic mass balance (Eq. 1) was used as the basis of the modelling, where the observed atmospheric mole fraction of CO2obs can be described as the sum of CO2 from individual sectors (CO2i) and a background contribution. This simple concept was adapted to the different CO2 isotopes by using the definition of the small delta (δ) value for 13CO2 and the definition of the large delta (Δ) 14CO2 as defined in Stuiver and Polach (1977). The simulated 13CO2 was calculated with Eq. (2) and the Δ14CO2 with Eqs. (3a), (3b). A detailed description on how Eqs. (2), (3a) and (3b) were derived can be found in Sect. S1 in the Supplement. 2δ13CO2=∑δ13CO2,i1000+1×12CO2i×13Rstd+13CO2,bg12CO213Rstd-1×1000. Here, δ13CO2i is the 13CO2 signature of emission source sector i (‰); 13CO2bg is the background 13CO2 abundance from the rolling (±30 d) median values of the MHD observations, 12CO2,i is equal to abundance of 12CO2 from sector i (mol mol-1) as simulated in TAC (Eq. 1); 13Rstd is the ratio of reference standard ((mol mol-1) / (mol mol-1)); and 12CO2 is the total 12CO2 enhancement (mol mol-1) from Eq. (1). 3aX=∑Δ14CO2,i1000+1×14Rstd1-2×25+δ13COi1000×12CO2,i12CO23bΔ14CO2=X×1-2⋅25+δ13CO2100014Rstd-1×1000, where Δ14CO2,i is the 14CO2 signature of emission source sector i (‰), 12CO2i is the abundance of CO2 from sector i (mol mol-1) from Eq. (1), 14Rstd is the ratio of reference standard ((mol mol-1) / (mol mol-1)), 12CO2 is the total CO2 mole fraction0 (mol mol-1) from Eq. (1); and δ13CO2 is the 13CO2 signature (‰) from Eq. (2).

The Δ14C is normalized to a δ13C value of -25 ‰; this is done to account for fractionation of the sample. Fractionation is the discrimination against one isotope in favour of the other in physical processes and chemical reactions. This discrimination takes place as the additional neutron in 13C alters both the weight of the carbon and their chemical bonding energies. Biological processes such as, for example, photosynthesis selectively favour the lighter isotope. Fractionation effects discriminate against 14C approximately twice as much as for 13C (Fahrni et al., 2017; Stuiver and Polach, 1977). Normalizing δ14C measurements to a common δ13C removes reservoir-specific differences that are caused by fractionation.

For this work, sector-specific emissions reported in EDGAR v4.2 from the year 2010 (Olivier et al., 2014) were used for the simulations of anthropogenic emissions and the National Aeronautics and Space Administration Carnegie Ames Stanford Approach (NASA CASA) emissions for biogenic emissions (Potter, 1999). It is assumed that all emissions reported in EDGAR correspond to 12CO2 emissions. A detailed list of source sectors and associated isotopic signatures can be found in the Supplement (Table S1). All fossil sources were considered to have a Δ14CO2 value of -1000 ‰.

The Δ14CO2 observations at TAC and MHD were used to calculate the recently added CO2 from fossil fuel burning (ffCO2). This method takes advantage of the fact that fossil fuels have been isolated from other carbon pools for so long that they are completely devoid of 14C; recent additions of CO2 from fossil fuel burning therefore lead to a depletion in the atmospheric Δ14CO2. We followed the approach of Turnbull et al. (2009a); this approach was chosen as the calculation of the uncorrected ffCO2 is separated from the corrections. This means that each correction can be evaluated for its impact on the final ffCO2 value individually. The equation given in Turnbull et al. (2009a) was adapted to have a correction term for heterotrophic respiration (Sect. 3.3.1) and emissions from the nuclear industry (Sect. 3.3.2), and is given in Eq. (4). The reasoning behind the need for the corrections for heterotrophic respiration and emissions from the nuclear industry are explained in detail in the next two sections. 4CO2ff=CO2,bg(Δobs-Δbg)(Δff-Δobs)-CO2hr(Δhr-Δobs)(Δff-Δobs)-CO2nuc(Δnuc-Δobs)(Δff-Δobs) Here CO2ff describes the recently added mole fraction from fossil fuel burning. CO2bg describes the background mole fraction. The rolling 15th percentile value (±20 d) of the high-frequency CO2 observations at MHD (background site) was used as CO2bg. For the Δbg, the rolling median value of the Δ14CO2 flask measurements at MHD were calculated within a time window of ±20 d of the Δobs. Figure S6 in the Supplement shows the MHD Δ14CO2 observations and the rolling median value of the data used as Δbg. The use of the 15th percentile for the high-frequency CO2 data and the median for the Δ14CO2 for weekly flask sampling (targeting background conditions) is consistent with the values used in the Δ14CO2 modelling in Sect. 3.1. CO2obs corresponds to the observed CO2 mole fraction in the flask measurements at TAC (polluted site), while Δobs refers to the Δ14CO2 measured from those same flasks. The Δff describes the 14CO2 signature of fossil fuel burning, and this was assumed to be -1000 ‰. Equation (4) also contains two correction terms, one for nuclear emissions and one for heterotrophic respiration. In addition to these two correction terms explained below, other work (Graven et al., 2012; Turnbull et al., 2009b) investigated corrections for cosmogenic 14C production and for the ocean–atmosphere CO2 exchange. For our work, both the ocean–atmosphere CO2 exchange and the cosmogenic 14C production were considered negligible as the corrections are generally small and not trivial to model. CO2hr corresponds to the mole fraction of CO2 at TAC that originates from heterotrophic respiration, while the Δhr is the Δ14CO2 signature of heterotrophic respiration; both values were obtained by models as described in Sect. 3.3.1. The Δnuc is the Δ14CO2 signature of pure 14CO2 emissions (Δnuc≈7.3×1014 ‰; Bozhinova et al., 2014) from nuclear sites and CO2nuc is the mole fraction of CO2 from nuclear emission at TAC (this value is obtained by modelling as described in Sect. 3.3.2). It is important to note that all approaches used to determine ffCO2 from Δ14CO2 observations make certain assumptions; the method used here and described in detail in Turnbull et al. (2009a) assumes that CO2 emitted from autotrophic respiration has the same Δ14CO2 signature as the observations (Δobs); Sect. 3.3.1 goes into more detailed as to why this is a reasonable assumption to make. All values used in the calculation of CO2ff, including the Δobs, and the Δbg and the correction terms have been included in Table S3.

For this work 12CO2, δ13CO2, and Δ14CO2 were simulated using Eqs. (1), (2), (3a) and (3b) at TAC and are compared with observations in Fig. 2. Daily mean values (24 h) are displayed for both the modelled (blue line) and the observed data (black line, points). The uncertainty estimate (light blue area) includes the baseline uncertainty as well as the emission inventory uncertainty. The uncertainties were investigated by calculating a Monte Carlo ensemble of model runs (4000 runs) with perturbed background concentrations and sector-specific emissions. The background concentration was randomly altered within a factor of 2 of the measurement uncertainty. The sector-specific emission maps were multiplied with a randomly generated matrix that let the emission in each grid cell vary between 50 % and 150 %. The shaded green areas represent the 95 % confidence interval uncertainty of these simulations. The TAC observations generally match the simulations well for 12CO2 and 14CO2. The exception is a large 12CO2 peak in November 2014 that is significantly underestimated by the model. During the same time period, the two 14CO2 samples taken were more depleted than the 14CO2 simulations.

The δ13CO2 simulations (Fig. 2) show comparatively large uncertainties; this uncertainty is dominated by the variation in the net ecosystem exchange flux (from NASA CASA) during the Monte Carlo runs described above. The variation in the net ecosystem exchange flux has an ostensibly larger influence on the 13CO2 simulations (compared to the 12CO2 and 14CO2) as carbon uptake and respiration cause strong fractionation in the atmosphere. This fractionation was captured in the model and the uncertainty estimation by assigning a δ13CO2 signature to the net ecosystem exchange flux (see Eq. 2 in Sect. 3.2 and Table S1 in the Supplement). The close fit of the observations to the median of the simulations indicates that the variability in the δ13CO2 signature of the net ecosystem exchange flux might have been overestimated.

For the 14CO2 simulations as shown in Fig. 2, the calculated uncertainty estimate was ±5 ‰ or ∼1.8 ppm in ffCO2 equivalent. The term fossil fuel equivalent is used to describe how much recently emitted fossil fuel would have to be present in a sample to cause the equivalent depletion in 14C in per mille (‰); the exact conversion from one to the other depends on the current atmospheric background level of CO2 and its isotopes. The uncertainty estimate of >±5 ‰ was predominantly influenced by the uncertainty in the 14CO2 background value, as this was chosen to be double the measurement uncertainty (>±4 ‰). This is not surprising as the Δ14CO2 observations have a large measurement uncertainty (1.8 ‰, ∼0.72 ppm ffCO2 equivalent) associated with them, and the measurement uncertainty was chosen as an indication of the background uncertainty. However, it emphasizes that strong ffCO2 signals are needed in order to obtain Δ14CO2 observations that can be distinguished from the background. At TAC, the fossil fuel influence is not always large enough to exceed this threshold.

This paper aims to determine if Δ14CO2 observations can be used to estimate ffCO2 at the TAC observation station in the UK. Multiple studies (Bozhinova et al., 2014; Graven and Gruber, 2011) have indicated that in some parts of the UK the radiocarbon method cannot be used as the large 14CO2 emissions from nuclear sites would mask the depletion in the atmospheric Δ14CO2 caused by recent fossil fuel emission. The flask sampling site in TAC was chosen deliberately following a preliminary study that suggested the influence from 14CO2 from the nuclear industry at the TAC was moderate.