In view of the overarching aim of reducing anthropogenic greenhouse gas emissions to mitigate climate change, reliable emissions data and timely information on emission reductions are indispensable, especially at the local scale in urban environments where emission reduction efforts are to be assessed. Of central importance in this context is the quantification of fossil fuel CO2 (ffCO2) emissions in cities as cities contribute more than 70 % to global and European ffCO2 emissions . Officially reported bottom-up emission inventories are usually based on statistical activity data, e.g., fossil fuel consumption, and emission factors for the different emission sectors, such as traffic or industry . Downscaled to urban and local resolutions, they form an important basis for policy decisions, as well as for fundamental research . Despite continuous improvements to such inventories, the benefits of bottom-up estimates are currently limited by their coarse spatial and temporal resolutions, large uncertainties in the available methodologies, and the delayed availability of data . To independently validate and refine emission inventories for CO2, atmospheric measurements providing timely, localized, and sector-specific top-down information are therefore indispensable.

The only method that allows direct measurement of vertical atmospheric trace gas fluxes is the eddy covariance (EC) technique, in which vertical wind velocity and trace gas concentrations are both measured at a frequency of 10 to 20 Hz e.g.,. Although this method assumes a horizontally flat and homogeneous surface area , studies have shown that EC measurements can also be successfully performed in a complex and heterogeneous urban environment . However, EC-based CO2 flux estimates contain fossil and non-fossil components. Models and measurements have shown that biospheric CO2 fluxes (autotrophic and heterotrophic respiration and photosynthesis) can contribute significantly to the total CO2 flux measured over an urban area, even in winter e.g.,. In addition, human respiration fluxes typically account for about 5 % of the total annual CO2 flux, depending on the population and emission density e.g.,. Considering the increasing use of biofuels as well e.g.,, this results in significant uncertainties in inverse estimates of fossil fuel emissions .

In separating fossil and non-fossil CO2 enhancements, radiocarbon has proven to be the ideal tracer since 14C-free fossil fuels dilute the atmospheric 14C/C ratio compared to a clean background e.g.,. To measure the atmospheric 14C/C ratio (on the order of 10⁻¹²), air is commonly sampled in glass flasks and subsequently analyzed in the laboratory, e.g., by accelerator mass spectrometry of the extracted and catalytically reduced CO2 . Based on long-term atmospheric 14CO2 observations, quantified the ffCO2 enhancements at three German sites and used the radon tracer method to derive ffCO2 fluxes for the respective catchment areas. analyzed the ratio of carbon monoxide (CO), which is co-emitted with ffCO2, to get a continuous time series of the excess ffCO2 concentration in Heidelberg, Germany, and used an atmospheric inversion model to obtain ffCO2 fluxes . used the mean ΔCO / ΔffCO2 ratio of flask pairs collected at two towers in Indianapolis, USA, to derive ffCO2 fluxes from CO fluxes measured by the flux gradient approach. However, to derive ffCO2 fluxes, all methods rely on the assumption of constant proxy / ffCO2 ratios or results from inversion models. Direct 14C-based ffCO2 flux measurements have not been possible so far because the precision and temporal resolution of state-of-the-art lasers for 14C in situ measurements are still far too low for EC measurements e.g., . The relaxed eddy accumulation (REA) method , on the other hand, allows for flux estimation from the concentration differences between two conditionally collected air samples, which can be determined in the laboratory. The ffCO2 fluxes can thus be estimated from the 14C-based ffCO2 concentration differences between updraft and downdraft flask sample pairs.

In the present study, to our knowledge, the first REA system for 14C-based estimation of ffCO2 fluxes was developed. Based on the principles of relaxed eddy accumulation (Sect. ) and 14C-based fossil fuel CO2 estimation (Sect. ), the purpose of this article is to describe the novel REA flask sampling system (Sect. ), as well as to evaluate its performance and assess the uncertainties of the concentration measurements (Sect. ). As a proof of concept of the 14C-based separation of fossil and non-fossil CO2 components, the ffCO2 concentration differences between updraft and downdraft flasks collected during a field campaign at a tall tower 112 m above ground level near the city center of Zurich, Switzerland, are presented (Sect. ). This work forms the basis for the derivation and analysis of ffCO2 fluxes in Zurich and for future deployments in other urban environments.

Relaxed eddy accumulation (REA), first described by , is a conditional sampling method for measuring turbulent trace gas fluxes using slow-response analyzers. A fast ultrasonic anemometer measures the vertical wind velocity w at a frequency of 10 to 20 Hz. Based on w, the opening and closing of two fast-response sampling valves are controlled in quasi-real time. Any bias in the vertical wind velocity must therefore be removed before activating the valves . When there is an updraft eddy and w is above a certain threshold w0, air is collected and accumulated in an updraft reservoir, whereas air is collected in a separate downdraft reservoir when w < -w0.

The range of wind speeds [-w0:w0] where no air is collected is called the deadband. Under ideal conditions, the mean vertical wind speed w‾ over a sampling period of, for example, 30 or 60 min is zero and defines the center of the deadband. The deadband width can be constant or dynamically adjusted in relation to the standard deviation of the vertical wind speed σw so that w0 = w‾+δσw . The larger the δ, the greater the concentration difference between the updraft and downdraft reservoirs, reducing the relative measurement uncertainty . In addition, a larger deadband reduces the switching frequency of the sampling valves, thereby increasing their lifetime . However, this also reduces the fraction of time during which air is collected, which reduces the sample volume and the statistical significance. A compromise between a high concentration difference, a sufficient sample volume, and good representativity has to be found . Since the requirement w‾ = 0 can be violated, particularly in urban environments with complex airflow, and since the actual value of w‾ is not known before the end of the sampling period, two options to trigger the valves based on vertical wind were implemented in this study (see Sect. ).

The flow rate into the two reservoirs is always zero when the valves are closed and constant when they are open. This relaxes the high technical requirements of the true eddy accumulation method proposed by , where the sampling rate is adjusted in quasi-real time in relation to the magnitude of the vertical wind velocity (for a detailed description, see , and ). However, the constant flow rate prevents a direct assessment of the mean vertical turbulent flux of a trace gas Fc. With REA, Fc is calculated according to Eq. () from the mean concentration difference between the updraft and the downdraft sample Δc, the standard deviation of the vertical wind speed σw, the mean molar air density ρm‾, and an empirical coefficient β. 1Fc=βσwρm‾c↑-c↓=βσwρm‾Δc

The proportionality factor β depends on the joint probability distribution of variations in the vertical wind velocity and the trace gas concentration . Without a deadband and under an ideal joint Gaussian distribution of w and c, β is 0.627 , but the dependence of β on the prevailing atmospheric conditions; the deadband width; and, eventually, the scalar, e.g., the trace gas concentration, itself adds uncertainty into the calculated flux . showed that, with a deadband dynamically adjusted based on the standard deviation of the vertical wind velocity, β does not depend on the atmospheric stability, allowing the use of a constant value in flux calculations. Consequently, assuming similarity in the turbulent exchange of two quantities, β can be determined with Eq. () from a scalar where the flux is known from EC measurements, e.g., temperature or CO2 .

Estimating the ffCO2 difference between updraft and downdraft reservoirs based on 14CO2 analyses of REA sample pairs and assuming scalar similarity between CO2 and 14CO2, Eq. () allows us to determine the fossil contribution to a total CO2 flux: 2FffCO2FCO2=ΔffCO2ΔCO2. In this paper, only the concentration differences (right-hand side of Eq. ) and their uncertainties are analyzed. The observation-based ffCO2 fluxes, which can be obtained by multiplying the ΔffCO2/ΔCO2 ratio of the REA samples with FCO2 from EC measurements, will be presented in a follow-up work.

It should be noted that Eq. () is unstable for FCO2 and/or ΔCO2 close to zero. In this case, a proxy other than CO2 is needed, e.g., CO. Moreover, like any other method based on the eddy covariance principle, REA only provides reasonable estimates of the mean vertical turbulent flux if the micro-meteorological conditions are stationary and if turbulence is well developed during the sampling period . If a temporal change in concentrations below the measurement height causes a significant storage flux, the measured turbulent fluxes are not representative of the respective surface fluxes at the time . Further, if vertical advection leads to significant flux components due to non-turbulent vertical transport, this cannot be properly captured by eddy covariance and the REA approach . This implies the consideration of various criteria when selecting suitable samples in any application (see Sect. ).

In determining the contribution of fossil fuel emissions to a measured CO2 signal, 14C has turned out to be an important tracer. The radioactive carbon isotope has a half-life of 5730 years. Consequently, the millions-of-years-old fossil fuels are 14C-free; hence, CO2 emitted by fossil fuel combustion (ffCO2) dilutes the atmospheric 14C/C ratio. Due to the low 14C abundance, the specific activity of a reservoir or sample is commonly given as the relative deviation (in ‰) from the absolute specific activity of the radiocarbon standard AABS = 0.2261 Bq gC⁻¹ (Eq. ) . This is commonly denoted as Δ14C but is abbreviated to Δ14 in this work to improve the readability of the following equations. 3Δ14=ASNAABS-1×1000 ASN is the 14C sample activity AS normalized to the postulated mean δ13C value of terrestrial wood of -25 ‰ to correct for isotopic fractionation due to biological or physical processes during the sample formation and the measurement routine : 4ASN=AS1-225+δ13C1000.

Following the general approach of and , any measured atmospheric 14CO2 signal can, analogously to the total CO2 concentration cmeas, be expressed as the sum of a background (bg), a fossil fuel (ff), a biofuel (bf), a nuclear (nuc), a stratospheric (strato), a respiratory (resp), a photosynthetic (photo), and an oceanic (oc) component: 5cmeas=∑ici,6cmeasΔ14=∑iciΔi14,i=bg, ff, bf, nuc, strato, resp, photo, oc.

On a local scale, as during REA sampling, it can be assumed that two air parcels differ only in terms of their fossil fuel, biofuel, respiration, and photosynthesis components, while the impact of the other, more distant sinks and sources is the same. Since biofuels and respiration have a similar Δ14 signature, they cannot be distinguished by radiocarbon analysis alone and are therefore summarized in the following as non-fossil (nf) CO2 emissions, with respiration being by far the largest contributor. Thus, the concentration differences between the updraft (↑) and the downdraft (↓) reservoir of an REA measurement can be expressed in the following way: 7cmeas↑-cmeas↓=cff↑-cff↓+cnf↑-cnf↓+cphoto↑-cphoto↓,8cmeas↑Δmeas14↑-cmeas↓Δmeas14↓=cff↑-cff↓⋅Δff14+cnf↑-cnf↓⋅Δnf14+cphoto↑-cphoto↓⋅Δphoto14.

Combining Eq. () and Eq. (), the difference in cff between updraft and downdraft reservoirs can be estimated via 9cff↑-cff↓=1Δphoto14-Δff14[cmeas↑(Δphoto14-Δmeas14↑)-cmeas↓(Δphoto14-Δmeas14↓)+(cnf↑-cnf↓)(Δnf14-Δphoto14)]. The corresponding uncertainty is derived according to Gauss' law of error propagation.

Since fossil fuel emissions do not contain any 14C, Δff14 is, by definition, exactly -1000 ‰. On the contrary, biogenic signatures are heterogeneous and much more uncertain (e.g., ). To estimate cff↑-cff↓ (in the following denoted as ΔffCO2), it is therefore necessary to make assumptions about Δphoto14, Δnf14 and cnf↑-cnf↓.

Since the Δ notation accounts for mass-dependent isotopic fractionation (Eq. ), Δphoto14 corresponds to the 14C signature of the photosynthesized atmospheric CO2. For our measurements of local CO2 fluxes close to the tall tower, Δphoto14 is therefore best approximated by the measured atmospheric signature Δmeas14. As there are always two flasks per REA run, the average of the up and down flasks is chosen: Δphoto14≈0.5⋅(Δmeas14↑+Δmeas14↓). However, due to temporal variability, the Δphoto14 uncertainty is larger than the measurement uncertainty (∼ 1.8 ‰; see Appendix ) and is therefore set to 10 ‰.

Non-fossil CO2 (from autotrophic and heterotrophic respiration and, to a lesser extent, biofuels) is generally more enriched in 14CO2 because heterotrophically respired CO2 and CO2 from biofuels were taken up by the biosphere several years to decades ago. At that time, the atmospheric Δ14 was higher due to 14CO2 released during nuclear bomb tests in the 1950s–1960s, which constituted the dominant contribution up to the 2000s . Since then, the strongest component of the ongoing atmospheric Δ14 decline has been the emission of fossil fuel CO2 . In total, the Δ14 signature of respiration was found to be larger than atmospheric values by a few tens of permil e.g.,. Following , an enrichment of the respiration-dominated Δnf14 of 25 ± 12 ‰ is assumed in this study. The atmospheric signature during CO2 uptake of the biospheric Δatmo14‾ is estimated by the mean Δmeas14 value in summer, when photosynthesis is most pronounced.

The third unknown is the difference Δcnf = cnf↑-cnf↓. This can be estimated based on the mean measured total CO2 differences between up and down flasks and the assumption that, in an urban setting, there is always a fossil contribution. Since this is only a very rough and upper estimate, a relative uncertainty of 100 % is reasonable.

The assumptions regarding Δphoto14, Δnf14, and Δcnf, as well as the specific values used to calculate ΔffCO2 from the REA flasks of the first measurement campaign in Zurich, are summarized in Table . Although Δphoto14, Δnf14, and Δcnf are not well known, the uncertainty in the ΔffCO2 estimates is dominated by the 14CO2 measurement uncertainty, which currently leads to an inherent ΔffCO2 uncertainty of 0.7 ppm at least and 1.2 ppm on average. Details are given in Appendix .

The relaxed eddy accumulation (REA) flask sampling system consists of an eddy covariance (EC) system with a 3D ultrasonic anemometer and an integrated open-path gas analyzer (IRGASON, Campbell Scientific Inc., Logan, UT, USA); two fast-response valves controlled by a solid-state DC control module (SDM-CD8S, Campbell Scientific Inc., Logan, UT, USA); a data logger (CR6, Campbell Scientific Inc., Logan, UT, USA); and an extension of a regular 24-port ICOS (Integrated Carbon Observation System) automated flask sampler, described, for example, in (Fig. ). This allows the collection of updraft and downdraft air samples (Sect. ) in glass flasks for subsequent laboratory analysis.

As depicted in Fig. , there are two inlets, one for updraft conditions and one for downdraft conditions. They are about 20 cm away from the center of the ultrasonic anemometer and are horizontally separated from each other by about 5 cm. The collection of air is controlled by the two solenoid valves located approximately 30 cm behind the inlets. They respond to the data logger's 20 Hz signal, which is based on the vertical wind velocity measurements of the IRGASON (Sect. ). This signal is also sent to the sampler computer, which controls the extended flask sampler. Two pumps (P_a, up and P_a, down in Fig. ) transfer the sampled air into two separate 50 L cylinders, which are called buffers in the following. The so-called loop systems (Sect. ) avoid flow rate fluctuations during sampling and non-sampling to ensure constant flow rates despite high-frequency switching. Excess air from the updraft and downdraft sides is released through one common outflow. After a successful sampling event, for which both 50 L buffers need to have a pressure between 1.2 and 1.6 bar (Sect. ), the samples are dried and transferred into 3 L glass flasks (pump P_b), and the buffers are evacuated again (pump P_c). Since this takes about 45 min, there is a second pair of buffers that can be filled in the meantime. This allows for a nearly continuous sampling routine. The flask pairs can be sent to the laboratory or re-sampled if, for example, the sampling conditions did not fulfill the requirements (Sect. ). In addition, a third line from the tower top directly to the flask sampler enables a simultaneous sampling of flasks with a regular 1/t filling , which can be used for quality control tests (Sect. ). In the following, the individual steps of collecting REA flasks are described in more detail. The following terminology is used: REA run denotes the REA sampling event of usually 1 h; REA ID denotes the unique, consecutively assigned number for each REA run; sampling mode denotes the state of the updraft or downdraft line when air is collected, i.e, when the vertical wind is above or below the deadband; and standby mode denotes the state of the updraft or downdraft line when no air is collected, i.e, when the vertical wind is below or above or within the deadband. A photo of the inlets and the extended flask sampler and specifications of the components of the system are shown in Fig.  and Appendix .

The final setup of the REA flask sampling system, including the chosen materials (Table ) and the flow scheme with the specially designed loop systems (Fig. ), was the result of many preliminary assessments, simulations, tests, and iterative system improvements required to meet the high technical requirements of the REA method and the sample analysis. However, due to non-idealities and uncertainties in the sampling procedure, the concentration of the air that is collected in the updraft and downdraft flasks may deviate from the “true” sample concentration that would result from a certain temporal variation in the gas concentration and the vertical wind velocity. To evaluate the performance of the system, i.e., to check for biases and quantify the uncertainty of the flask concentrations due to the sampling process, several experiments and simulations were performed. This section describes the following: 5.1quality control tests inthe laboratory ensuring thatthe collected air is generallytransferred into the glassflasks without contamination5.2simulations using20HzCO2in situ measurements inZurich to estimate biases anduncertainties inΔCO2flaskmeasurements due tonon-idealities in the sampling processTable 3:MeanΔCO2uncertainties5.3quality control tests performed during the Zurichcampaign and comparison of measured flaskconcentrations with in situ measurements to assessthe quality of the samples collected in Zurich. The focus was on the uncertainty in the CO2 concentration differences between updraft and downdraft flasks (ΔCO2) rather than on absolute concentrations because only the concentration differences are needed to calculate fluxes (Eq. ). Moreover, the flask concentration differences were comparable with high-frequency in situ CO2 measurements of the IRGASON and a multi-compound (MGA⁷) gas analyzer (MIRO Analytical AG, Wallisellen, Switzerland) despite an irregular calibration of the gas analyzers. It must be noted that, when estimating fossil fuel CO2 differences, uncertainties due to the sampling process are negligible compared to the 14C measurement uncertainty (compare Sect.  and Appendix ).

Figure  shows the differences in CO2 and ffCO2 between the updraft and downdraft flasks, measured with the gas chromatograph at the ICOS FCL in Jena and derived from the 14CO2 analyses at the ICOS CRL in Heidelberg (Eq. ). Of the 103 REA flask pairs selected for laboratory analysis and analyzed for CO2 at the FCL (Sect. ), 3 samples were lost during graphitization at the CRL. Eight sample pairs from the end of the campaign were not analyzed for 14CO2 because their total CO2 difference was small, and the expected significance of the 14CO2 analysis was low compared to the associated costs. This leaves a total of 92 ΔffCO2 estimates. The error bars represent the measurement uncertainties (ΔCO2 uncertainties of about 0.05 ppm in x direction are omitted for clarity). In the analysis of ffCO2, uncertainties due to the sampling process were considered to be negligible (Sect. ). The colors indicate the month in which the sample was collected.

It can be seen that the largest concentration differences between updraft and downdraft flasks with ΔCO2 of up to 13.6 ppm were collected in February and March, when anthropogenic emissions are usually higher than average due to residential heating. Most of these samples are close to the 1:1 line, which represents the case where the net non-fossil CO2 flux is zero and the measured CO2 fluxes are completely due to fossil fuel emissions. Accordingly, the observed deviations from this line to the right or the left indicate dominant respiratory and other non-fossil sources or photosynthetic signals, respectively. For samples along the x axis, the ffCO2 contribution is approximately zero. In agreement with other studies e.g.,, this shows that there are significant non-fossil CO2 signals even in winter.

It should be noted that the applied sample selection criteria do not necessarily exclude sampling periods in which a change in the storage below the sampling height contributes to the measured fluxes. This is the case, for example, when the depth of the atmospheric boundary layer increases rapidly due to convective, turbulent vertical motions generated by radiative heating of the surface in the morning . Based on an observed drop in CO2 concentration in the morning and a preliminary investigation of the turbulence structure of the atmosphere, some of the Zurich REA flasks with large CO2 concentration differences between updraft and downdraft samples were probably collected during this time. In this case, the composition of the samples does not necessarily represent the actual surface fluxes during the REA sampling periods but rather represents the integrated nocturnal fluxes. Further interpretation of the results and a subsequent investigation of the corresponding CO2 fluxes therefore require a thorough analysis of the sampling periods.

What also becomes clear in Fig.  is that most signals are of the order of 1 ppm or less, which is small compared to the ΔffCO2 uncertainty. The latter was, on average, 1.2 ppm and was primarily due to the mean 14CO2 measurement precision of 1.8 ‰ (Appendix ). Consequently, ffCO2 flux estimates derived from samples with ΔffCO2 < 1.2 ppm will mostly have uncertainties of more than 100 % (compare to Eq. ). This highlights the importance of further quality control of the existing data set for subsequent calculations and quantitative analyses of ffCO2 fluxes.

A relaxed eddy accumulation (REA) flask sampling system for 14C-based estimation of ffCO2 fluxes for urban eddy covariance (EC) flux measurements was developed and tested in the ICOS Flask and Calibration Laboratory in Jena, Germany, and on a tall tower near the city center of Zurich, Switzerland.

Two fast-response valves are activated by the vertical wind signal from an ultrasonic anemometer of a co-located IRGASON. The conditionally collected air accumulates in two separate cylinders (one for the updraft sample and one for the downdraft sample) and is transferred into 3 L glass flasks after the sampling period using an automated 24-port flask sampler. The samples can thus be analyzed in the laboratory for a variety of gases, including 14CO2. Laboratory tests and quality control tests during the first measurement campaign in Zurich showed that the sampling procedure does not cause a significant bias in the CO2 differences between updraft and downdraft samples. Uncertainties due to the sampling process are negligible when estimating fossil fuel CO2 differences between the updraft and downdraft flasks and, consequently, ffCO2 fluxes as these are dominated by the 14CO2 measurement precision. The novel REA flask sampling system itself fulfills the high technical requirements of relaxed eddy accumulation, providing high-quality data for scientific studies of multiple non-reactive species.

Due to the prerequisites of the EC and REA method, e.g., stationarity and well-developed turbulence, and the costs and efforts associated with the flask analysis, only a limited number of individual sampling periods can be analyzed. In general, operating the system, i.e., scheduling sampling events, analyzing and selecting suitable sampling periods, sending the flasks to the laboratory, etc., requires frequent remote and on-site work.

Given the good agreement between the total CO2 concentration differences measured in the REA flask sample pairs and observed from in situ measurements of an MGA⁷, the results of the first measurement campaign in Zurich serve as a proof of concept for a 14C-based separation of fossil and non-fossil CO2 signals. As expected, the CO2 differences between updraft and downdraft samples were largest during the heating season in February and March. In this case, fossil fuel emissions were the major contributor. However, even in winter, small photosynthetic and significant non-fossil (respiration and biofuels) signals were observed, highlighting the role of the biosphere in an urban environment.

The main challenge so far was a generally small signal-to-noise ratio of measured 14CO2 differences. Resulting ΔffCO2 uncertainties on the order of 100 % limit the interpretation of individual results. However, a new accelerator mass spectrometer has reduced the Δ14 measurement uncertainty and, thus, the ΔffCO2 uncertainty by about 23 %, which will increase the fraction of usable samples in future applications.

Two improvements are proposed to further increase the concentration differences in future campaigns: first, the two pumps in the loop systems are recommended to be replaced by larger pumps with a higher pump speed, allowing a reduction in the proportion of time that air is collected and, thus, a larger deadband width δ. Second, the so-called hyperbolic relaxed eddy accumulation could be added into the logger program. With this setting, as proposed by , air would only be collected if the fluctuations in vertical wind speed w′ and concentration c′ are above a certain threshold. For the latter, the 20 Hz CO2 measurements of the IRGASON could be used. Excluding eddies with little flux contribution increases the concentration differences more effectively than a linear deadband with larger deadband width and is recommended for scalars where the detection limit is of concern . However, the hyperbolic deadband comes with additional challenges as the threshold for not only vertical wind velocity fluctuations but also CO2 mixing ratio fluctuations would need to be dynamically adjusted. The signal-to-noise ratio could also be increased if multiple graphite targets were to be analyzed or if measurements were to be taken closer to a particular source. However, obtaining and analyzing multiple flask samples would require major changes in the setup of the flask sampler and would multiply the cost and instrument time accordingly. In addition, analyzing turbulent fluxes on a neighborhood scale requires tall-tower measurements within the inertial sublayer. Besides limitations in the availability of the corresponding infrastructure, reducing the measurement height was therefore not an option for our study.

The next step in the process will be to derive the actual ffCO2 fluxes using EC-based total CO2 fluxes and assuming scalar similarity to estimate the β coefficient for each sampling period individually (Eq. ). This will allow for a fully independent time-resolved evaluation of the Zurich emission inventories, taking into account the changing turbulent flux footprints during each of the sampling intervals. Furthermore, the analysis of CO and other species in the updraft and downdraft samples along with 14CO2 will provide guidance regarding the use of co-emitted species for partitioning total CO2 fluxes into fossil and non-fossil components.