Fossil and non-fossil components of the CO2 flux measurements were separated by 14CO2 analysis of flask sample pairs conditionally collected using the REA flask sampling system described in detail in . In summary, depending on the 20 Hz vertical wind measurements of the IRGASON's 3D ultrasonic anemometer (Sect. ), air was collected through two co-located inlets with two fast-response valves into two separate reservoirs: one for updrafts, and one for downdrafts. After a sampling period of, e.g., 60 min, it was checked whether sufficient air has accumulated for a subsequent CO2 and 14CO2 analysis in the laboratory. If so, the accumulated air was transferred by an extended automated 24-port flask sampler into two 3 l glass flasks that could be analyzed in the laboratory (denoted as “successful” REA measurement in the following). Updraft and downdraft were thereby defined with respect to the mean vertical wind velocity w‾, excluding a range of wind speeds centered around w‾ and scaled by the standard deviation of the vertical wind σw (scaling factor δ). This so-called deadband with half-width δ⋅σw was intended to increase the concentration difference and to reduce the number of valve switchings . w‾ and σw were either calculated from the 30 min period before sampling start (pre-set deadband) or dynamically adjusted using a 15 min backward-looking averaging interval (dynamic deadband). The latter lead to a more equally distributed sampling of updrafts and downdrafts and was therefore better suited for changes in vertical wind statistics during the sampling period. The calculated fluxes are independent of the method used to compute the deadband, since this is taken into account in the β coefficient (see below) . See for technical details on the REA sampling.

Due to the costs and logistics associated with flask sample analysis, only a limited number of successful REA measurements could be analyzed. The selected REA flask samples were analyzed for CO2 in the ICOS (Integrated Carbon Observation System) Flask and Calibration Laboratory in Jena, Germany, and for 14CO2 in the ICOS Central Radiocarbon Laboratory in Heidelberg, Germany. Based on these measurements, the ffCO2 differences between updraft and downdraft samples, in the following denoted as ΔffCO2, were estimated (Appendix , ). Under stationary and well-developed turbulence, the ffCO2 flux FffCO2 can then be estimated according to Eq. (): 1FffCO2=βσwρm‾ΔffCO2. ρm‾ is the mean molar air density in molm-3. The proportionality factor β depends on the joint probability distribution of variations of the vertical wind velocity and the gas concentration and on the deadband width e.g.,. Values <0.1 or >1 indicate non-ideal sampling conditions for REA measurements . Due to the availability of co-located EC measurements of net CO2 fluxes (Sect. ), these measured CO2 fluxes were used to calculate β for each sampling period individually: 2β=FCO2σwρm‾ΔCO2. ΔCO2 is the CO2 concentration difference between updraft and downdraft flask samples measured in the laboratory and FCO2 is the net CO2 flux measured by EC (Sect. ). Assuming scalar similarity between CO2 and 14CO2, Eq. () can be inserted into Eq. (): 3FffCO2=FCO2ΔCO2⋅ΔffCO2=ΔffCO2ΔCO2⋅FCO2. Accordingly, the fossil contribution to the net CO2 flux equals the ΔffCO2 / ΔCO2 ratio of the REA flask samples. The uncertainty of the ffCO2 flux was derived according to Gauss' law of error propagation from Eq. (). For ΔCO2 and ΔffCO2, only the measurement uncertainties from the laboratory analysis were considered, as uncertainties due to the sampling process, e.g., a time lag between a change in vertical wind and a switching of the fast-response sampling valves, are negligible compared to the 14CO2 measurement uncertainty . The uncertainty of FCO2 was estimated using the random uncertainty estimate from EddyPro (Sect. ). Additional uncertainties, e.g., due differences between IRGASON and MGA⁷ measurements, differences between different EC data processing options, due to the assumption of scalar similarity or due to turbulent sampling error in the REA flask concentration differences, were considered less relevant and not taken into account.

It is important to note that Eq. () describes the turbulent fluxes at the measurement height. These fluxes only represent the surface fluxes if changes in the storage below the measurement height are negligible and there is no mean vertical advection. While this is usually the case during well-mixed, convective conditions (i.e., in the afternoon), significant storage fluxes can occur, particularly in the morning hours during the transition from low-turbulence, nighttime conditions to well-developed turbulence, when the depth of the atmospheric boundary layer increases and built-up CO2 is vented from the layer below the measurement height e.g.,. A storage correction, as it is recommended and commonly applied in EC measurements e.g.,, would require knowledge of both the storage flux FCO2,strg and the ffCO2 / CO2 ratio of the storage fluxes. However, the magnitude of the storage flux in cities, especially in the morning, is associated with significant uncertainties . The ffCO2 contribution to the storage fluxes equals the ratio of the flux averages over the period during which CO2 accumulated below the measurement height. For negative storage fluxes, i.e., the venting of CO2 which accumulated prior to the measurement period, the ffCO2 / CO2 ratio will therefore not necessarily equal the surface flux ratio during the measurement period. Consequently, a meaningful, observation-based storage flux correction for the REA measurements is not feasible. Thus, the presented fluxes are not corrected for changes in storage. While REA measurements during or after low-turbulence conditions therefore do not reflect the surface fluxes during the sampling period, the measured ffCO2 / CO2 ratio still provides information about the average relative contribution of fossil fuel emissions in the time period since the layer below the measurement height became decoupled prior to the start of the REA measurement – usually a nocturnal accumulation under low-wind conditions. Therefore, measurements with low turbulence and/or storage fluxes are analyzed separately. The criterion used in this study to flag the corresponding measurements is described in Sect. .

As the 14CO2 differences between updraft and downdraft samples collected in Zurich and Paris were often close to or smaller than the detection limit in the laboratory analysis, the REA system was modified, as suggested in . To enable the use of a larger deadband width, larger pumps were installed in the REA system before the campaign in Munich. This was necessary because a larger deadband width reduces the proportion of time during which air is collected and therefore increases the required sampling flow rate needed to collect enough air for laboratory analysis. In addition, the option for hyperbolic relaxed eddy accumulation (HREA, ) was added. In HREA, air is only collected if both vertical wind velocity fluctuations w′=w-w‾ and fluctuations in the scalar concentration c′=c-c‾ are above a certain threshold, which is characterized by the hole size H (similar to δ and a pre-set or dynamic deadband in normal REA). This maximizes the concentration differences between updraft and downdraft reservoirs, as only the eddies that contribute the most to the vertical flux are sampled, and is recommended for REA applications where sampling differences are close to the detection limit .

To ensure high quality measurement data, the performance of the REA flask sampling system was tested regularly (for details, see ). To examine biases between updraft and downdraft sampling, a pair of quality control flasks was sampled about once a month by continuously collecting air through both updraft and downdraft lines without switching the valves. Simultaneously, a third flask was sampled through a separate line directly into the flask sampler, bypassing the reservoirs where updrafts and downdrafts accumulate. If the system was operating as intended, the concentrations of the three quality control samples should agree within the WMO compatibility goal of 0.1 ppm for CO2 (WMO recommendation for compatibility of measurements of greenhouse gases and related tracers, ).

To verify the correct switching between updraft sampling, downdraft sampling, and no sampling, the measured CO2 concentration differences between the updraft and downdraft REA flask pairs were compared to the CO2 in situ measurements of the IRGASON and the MGA⁷. For this purpose, the high-frequency gas densities were converted to dry molar fractions and averaged over the respective actual sampling times, as described in .

To detect technical problems as early as possible, automated leak and critical component tests were carried out daily in the Paris and Munich campaigns. The results of the quality control flask measurements are given in Appendix .

Besides technical requirements, REA is like any other turbulent flux measurement technique restricted to certain micrometeorological conditions, e.g., stationarity and well-developed turbulence . Moreover, and in contrast to the EC technique, REA measurements cannot be processed retrospectively, e.g., cannot be corrected for changes in the mean vertical wind velocity. Therefore, additional criteria are necessary . Several criteria have already been considered in the selection of suitable flask samples during the campaigns . However, due to the limited number of good sampling conditions in the urban environment, the refinement of EC processing options, and the addition of further criteria after the measurement campaign, the analyzed sampling periods were not always ideal for REA measurements. For analysis of the results, the measurements were characterized based on five flagging criteria (Table , see Appendix for details). Based on these criteria, the analyzed REA measurements were classified into three categories (Fig. ). “Well-mixed measurements” are assumed to best represent the surface fluxes during the sampling period. These measurements are the most valuable for answering our research questions and were analyzed in the most detail. In contrast, “low-turbulence and storage measurements” are probably not representative of the surface fluxes during the sampling period due to insufficient turbulence or changes in storage below the measurement height (Sect. ). However, the relative ffCO2 contributions were investigated to characterize the integrated fluxes before and during the sampling period. Measurements with QC =2, β<0.1, β>1 or SNR <100 % were not considered further in this study.

To analyze the flux source areas during the individual REA measurements, flux footprints were derived for each 30 min averaging interval using the flux footprint model of . Inputs were turbulence data from eddy covariance measurements , boundary layer height ERA5 reanalysis estimates from the Copernicus Climate Change Service , measurement heights and tower coordinates, and roughness length and displacement height derived from building and vegetation height maps. Details on the flux footprints are provided in .

For the 30 min time periods during which well-mixed REA measurements were taken, aggregated footprints were calculated. These aggregated footprints were combined with the WorldCover product provided by the European Space Agency (https://esa-worldcover.org, last access: 12 December 2025) to derive comparable mean land cover fractions using the same data source for each city. The flux footprints were also used to identify measurements which were potentially influenced by emissions from a district heating plant in Zurich and a brewery in Munich by calculating the expected flux contributions from the corresponding areas of interest (Appendix ).

To generalize and quantify the results from the individual REA measurements, the mean ffCO2 / CO2 flux ratios R‾ffCO2 and the mean magnitude of the nfCO2 fluxes F‾nfCO2 were determined for each city. Due to the small number of measurements, it was not possible to fully account for the spatial and temporal variability. We distinguished between summer and winter measurements, and excluded measurements which were potentially influenced by large point-source emissions. In this work, “summer” refers to the period from July to October, and “winter” to the period from November to April (inclusive). This seasonal division of the measurement campaigns aligns roughly with the shift between European summer and winter time and with the change in local emissions due to heating degree days, and is consistent with other studies conducted in the same location during the same period . If ffCO2 and CO2 fluxes were perfectly linearly correlated, the mean ffCO2 / CO2 ratios would be best described by the slope of an error-weighted total least squares regression line . Due to generally low correlations of the observed REA fluxes, however, R‾ffCO2 was determined as the error-weighted mean of the individual ffCO2 / CO2 ratios. To minimize the uncertainty, the individual RffCO2 values were calculated directly from the flask measurements as ΔffCO2 / ΔCO2, i.e., completely independent of the EC flux measurements (compare Eq. ). RffCO2>100 % indicates a negative nfCO2 flux, i.e., photosynthetic uptake, while RffCO2<0 % is physically unreasonable and only observed if ΔffCO2 is slightly negative within its measurements uncertainties. In addition, the mean and variability of the nfCO2 fluxes were examined. A z-test was used to evaluate whether the observations were significantly different from R‾ffCO2=100 % or FnfCO2=0 µmol m⁻² s⁻¹ (significance level of 0.05), i.e., completely fossil CO2 fluxes, taking into account the mean measurement uncertainties. To meet the assumption of normal distribution, only measurements with relative ΔCO2 uncertainties ≪1 were considered (most, but not all, of these samples were already excluded by the consideration of the signal-to-noise ratio as defined in Sect. ). See Appendix for details.

While the REA flask measurements aimed to analyze turbulent ffCO2 fluxes at the urban neighborhood scale, the absolute flask concentrations also contain information about the fossil and non-fossil CO2 enhancements compared to clean background air and thus about the composition of CO2 fluxes in a broader continental region, including other urban areas and regional emission sources. Following , we calculated the ffCO2 excess from the mean CO2 and Δ14C values of the up- and downdraft REA sample pairs, using the corresponding concentration measurements at the European marine background station Mace Head on the western coast of Ireland as background concentrations, and assuming that the biogenic Δ14C signature equals the background concentration (see Appendix ). Second-order effects, such as 14C-enriched heterotrophic respiration and nuclear contamination , were not considered because the necessary concentration footprints were only available until the end of 2023, and the corrections are negligible for our analysis. For details and an evaluation of these corrections on the Zurich measurements, we refer to and Appendix . The mean ffCO2 / CO2 ratios of the excess concentrations thus represent the average contributions of ffCO2 emissions to the CO2 fluxes on the trajectories between Mace Head and the three measurement sites.

A qualitative analysis of the observed ffCO2 fluxes from the well-mixed REA measurements, in relation to net CO2 fluxes and the time of day (Fig. ), shows that due to the selection of samples with large SNR the dataset is biased towards high fluxes. While the large CO2 fluxes clearly differed in composition between the three sites, the separation of smaller fluxes was limited by measurement uncertainties, particularly in Zurich and Paris.

The continuous EC measurements showed that the CO2 fluxes were, on average, as expected higher in winter than in summer, especially during the day, pointing at increased emissions and reduced photosynthetic uptake. The differences were most pronounced in Paris, where in summer the median turbulent flux between 12:00 and 17:00 LT was approximately zero. This means that in 50 % of the considered time periods, negative CO2 fluxes, i.e., photosynthesis, were larger than positive CO2 fluxes through respiration and anthropogenic emissions. Seasonal differences are also evident in the REA ffCO2 measurements. In Zurich and Paris, ffCO2 fluxes were, on average, much smaller in summer than in winter. However, the representativity of the results is limited by the small number of well-mixed measurements, particularly in summer. It should also be noted that negative ffCO2 surface fluxes are unreasonable and are attributed to the limited resolution of small 14CO2 differences between updraft and downdraft samples (the error bars indicate the 1σ uncertainties). Nevertheless, the measurements are shown here, because they have a significant nfCO2 component (SNR >100%). The fact that far fewer negative ffCO2 flux data points were measured in Munich than in Zurich and Paris highlights the improvement in the REA measurements in Munich. In Munich, the difference between summer and winter measurements was much smaller, despite comparable mean air temperatures during the REA measurements to those in Zurich and Paris (Table ). This could be related to the relatively large proportion of buildings in the footprint of the Munich tower that are heated by district heating.

Compared to the median CO2 fluxes, the fluxes during the selected REA sampling periods were often exceptionally high. This indicates that the dataset is biased towards high fluxes, caused by the systematic selection of flask pairs with large CO2 concentration differences to increase the potential ffCO2 signal. In Zurich, all of the analyzed fluxes that exceeded the 75th percentile of the continuous EC fluxes (denoted as P0.75 in the following) were measured in winter and were almost entirely due to fossil fuel emissions. In Paris, there were only five REA measurements with FCO2>P0.75. As in Zurich, they were measured in winter, but they were not as clearly dominated by fossil fuel emissions as the large winter fluxes measured in Zurich. In Munich, turbulent fluxes >P0.75 were analyzed in both summer and winter, and most had a significant positive nfCO2 component. Thus, while the large fluxes represent relatively rare conditions, the high signal-to-noise ratio (which was the main reason for analyzing them) allows observation of differences in the composition of the fluxes between the three cities (cf. Sect.  and ).

REA measurements conducted in Zurich and Paris when CO2 fluxes were below P0.75 showed positive and negative nfCO2 components of up to ±45 µmol m⁻² s⁻¹. However, the uncertainties were large and there were very few summer measurements, as most of the measurements were flagged because of SNR <100%, β<0.1 or β>1. In Munich, on the contrary, the uncertainties were much smaller (see Table ) and, except for a few measurements, all measurements showed positive nfCO2 components. This means that respiration and biofuel emissions were generally larger than photosynthetic uptake. The latter is consistent with the observations from the continuous EC measurements that the net CO2 fluxes were highest in Munich and mostly positive throughout the year.

The correlation between the ffCO2 and CO2 fluxes was largest (0.68) for the Zurich winter measurements (Table ). However, no clear correlation was observed when only the measurements with FCO2<P0.75 were considered. This could be caused by a large biospheric signal, a large temporal or spatial variability and/or an insufficient signal-to-noise ratio. To investigate the cause more closely, spatial patterns and expected effects of measurement uncertainties are discussed in Sect.  and .

Extraordinarily large CO2 fluxes analyzed in Zurich and Munich showed different compositions (Sect. ). While the Zurich fluxes were mostly fossil, the Munich fluxes contained a surprisingly large nfCO2 component. Based on the mean wind directions and modeled flux footprints, we found that these measurements were likely affected by fossil fuel emissions from a district heating plant in Zurich and non-fossil emissions from a fermentation process in a brewery in Munich, respectively. The conclusive results indicate high quality of the REA and EC measurements, and the footprint analysis. Moreover, these point-source influenced measurements highlight the challenges involved in interpreting atmospheric observations in a complex urban environment.

In Zurich, the net CO2 fluxes observed with wind from the west were generally smaller than those with wind from the east (Fig. a). The CO2 fluxes >P0.75, which were clearly dominated by fossil fuel emissions (Fig. b), were observed from about 70 and 135° N. This is consistent with the high proportion of vegetated areas in the west, in contrast to the city center, a district heating plant, and arterial roads in the east (Sect. ). Based on analysis of the flux footprints and the operating times of the district heating plant, we identified 10 measurements from the southeast that were potentially influenced by emissions from the district heating plant. See Appendix  for details.

In Paris, measurements were primarily taken during south-southwesterly wind. Due to the sparse data coverage, no spatial patterns could be investigated. There is no evidence of any distinct point-source emissions that could have affected the REA measurements. For completeness, the corresponding directional figures for Paris are shown in Appendix .

In Munich (Fig. ), the highest CO2 fluxes were measured when the wind came from southeast-east. Located in this direction are a brewery, the central railway station, and the historic city center (∼0.3, 1, and 2 km horizontal distance, respectively, see Sect. ). Striking are the large nfCO2 fluxes of up to 50 µmol m⁻² s⁻¹. The fact that biospheric and human respiration fluxes are typically much smaller e.g., indicates a non-respiratory anthropogenic nfCO2 source. Footprint analyses of the respective measurements, using the model of , showed that the brewery was within the peak area of the flux footprint (Appendix ). Therefore, we assume that the large nfCO2 emissions from the southeast-east resulted from a fermentation process . As there is no information available regarding operating times or the temporal emission profile of the brewery, all measurements with a substantial flux contribution from the brewery area, as estimated from the flux footprints, were considered to be potentially influenced by these large non-fossil point-source emissions (see Appendix ). Apart from measurements from the southeast, all nfCO2 fluxes >20 µmol m⁻² s⁻¹ were measured in the early morning. As discussed in Sect. , this could indicate an unaccounted contribution from storage fluxes, further supported by the uncertainties in the distinction between low-turbulence/storage and well-mixed conditions (Sect. ).

The measurements provide confidence in the EC and REA measurements as well as in the footprint analysis, and could be used to validate or refine bottom-up emission estimates of the respective point sources. Non-fossil CO2 emissions from fermentation processes in breweries, for example, are usually not included in emission inventories. For the characterization of the usually smaller CO2 fluxes and the analysis of the biospheric nfCO2 fluxes, however, these measurements need to be excluded.

When the measurements potentially influenced by the large CO2 emissions from a district heating plant and a brewery near the measurement sites in Zurich and Munich were excluded, the error-weighted mean ffCO2 / CO2 flux ratios of the well-mixed measurements were approximately 50 % or less in summer and 80 % to 90 % in winter. In Zurich and Paris, however, the significance and representativeness of the results were limited by the small number of measurements. In Munich, on the contrary, average nfCO2 contributions were significantly greater than zero, particularly in the early morning in summer. This highlights the improvements achieved in the REA measurements and the importance of considering nfCO2 fluxes in cities.

In Zurich, no significant average nfCO2 signal (p-values >0.05) was observed. In summer, the mean ffCO2 / CO2 flux ratio was 48±52 % and the mean absolute nfCO2 flux was 0±4 µmol m⁻² s⁻¹. The significance of the results was mainly limited by the small number of well-mixed measurements (N=3). In winter, the mean ffCO2 contribution of the Zurich samples was 92±11 %. To resolve the presumably small mean nfCO2 component, many more measurements and/or smaller measurement uncertainties would have been necessary (see Appendix ).

In Paris, the eight selected summer samples showed mostly non-fossil CO2 contributions. The negative mean ffCO2 ratio could be explained by the ffCO2 flux uncertainties (compare Fig. ), but a larger ffCO2 contribution was expected. Note that most of the measurements were conducted in the early morning. Therefore, storage fluxes cannot be ruled out. However, due to the small number of samples, a further subdivision of the measurements into morning and afternoon measurements, for example, was not feasible. Similar to the Zurich measurements, the Paris measurements were generally more successful in winter than in summer due to larger signals. The mean ffCO2 contribution in winter was 80±10 %, meaning that, on average, about 20 % of the observed CO2 emissions were due to positive nfCO2 fluxes.

In Munich, the higher data quality and greater number of measurements enabled the detection of significant nfCO2 contributions in both summer and winter. The larger nfCO2 fluxes observed in summer compared to winter were primarily attributed to the measurements taken in the early morning during summer. When only 18 summer measurements taken after 11:00 LT were considered, R‾ffCO2 was 64±6 % and F‾nfCO2 was 5.6±1.3 µmol m⁻² s⁻¹, which is much smaller than for the early-morning measurements and comparable to the winter measurements. In winter, no significant differences were observed between measurements taken before and after 11:00 LT. This could be explained by larger respiratory fluxes and nfCO2 dominated storage fluxes in the morning (Sect. ) and larger photosynthetic uptake, i.e., negative nfCO2 fluxes in the afternoon. This temporal variability is larger in summer than in winter. With the reduced measurement uncertainties, about 50 to 100 REA measurements are sufficient to identify average nfCO2 fluxes of the order of 10 % or 3 µmol m⁻² s⁻¹ at a 0.05 significance level (Appendix ).

Overall, it is remarkable that the mean nfCO2 contributions are positive in all three cities, both in summer and in winter. Only a few measurements show a significant negative nfCO2 flux. This contrasts with various studies that estimated negative nfCO2 fluxes in urban areas, particularly during the warm growing season but also during the cold dormant season e.g.,. The positive nfCO2 fluxes in our study could be explained, for example, by the low proportion of vegetated area within the flux footprints. However, the differences in F‾nfCO2 between the three cities could not be attributed to the respective average vegetated area, which was slightly larger in Zurich than in Paris and Munich (Table ). It should be noted that the observed nfCO2 fluxes include human respiration. According to bottom-up estimates for 2022, the mean annual human respiration fluxes within a 2×2 km2 square around the measurement sites are about 2.5 µmol m⁻² s⁻¹, or 10 % of the net CO2 fluxes in all three cities . For comparison, the estimated human respiration flux in the footprint of the study by was only 0.22 µmol m⁻² s⁻¹. Human respiration could therefore account for a significant proportion of the observed nfCO2 fluxes. Moreover, due to the small number of analyzed samples and the systematic selection of samples with presumably large concentration differences, the results may be biased toward periods with positive nfCO2 fluxes. As a further analysis, a 1:1 comparison of the REA fluxes with the emission inventories and biospheric models, taking into account the respective flux footprints, could be useful. As the example of the high nfCO2 fluxes from the direction of a brewery in Munich shows, the measurements could also be influenced by other anthropogenic nfCO2 point sources. In Munich, for instance, there are also other, more distant breweries. Based on our flux footprint analysis, we excluded all measurements where one of these breweries could have impacted the measured flux. However, excluding these measurements had no significant impact on the results (not shown here). Consistent with the aforementioned studies, our measurements underscore the importance of nfCO2 fluxes in urban areas.