Carbon uptake of an urban green space inferred from carbonyl sulfide fluxes

Introduction

As a consequence of climate change, cities seek ways to carbon neutrality. In order to verify carbon emission reductions, atmospheric measurements are crucial. Measurements of greenhouse gas concentrations and emissions can be made with many different methodologies and in a variety of scales extending from local-scale eddy covariance (EC) measurements^1,2 to city-level tall tower and total column measurements^3,4,5. From the different observational methods, EC is the most direct technique to quantify urban emissions by providing the carbon dioxide (CO₂) net exchange (NEE) between a land area and the atmosphere almost continuously. However, partitioning NEE into different flux components is critical to quantifying the anthropogenic emissions and for a comprehensive understanding of the contribution of urban areas to climate change. One of these components is the carbon assimilation, i.e., gross primary production (GPP) of urban vegetation, which takes up part of anthropogenic emissions and thus obscures emission signals⁶. In the absence of anthropogenic emissions GPP can be estimated by subtracting ecosystem scale respiration (R) and NEE (see GPP_EC in Eq. (7)). In a human-influenced context, however, CO₂ emissions cannot be neglected, but they reveal a pitfall of the simple GPP_EC methodology: It cannot recognize which NEE data have been influenced by anthropogenic CO₂ emissions, and thus cannot be used in an urban context. Consequently, measurements of urban GPP have been residual estimations⁷ or are based on light-response curves⁸, but direct observations have been missing.

Carbonyl sulfide (COS) is a gaseous compound naturally found in the atmosphere, with an average mixing ratio between 440 and 500 ppt⁹ (10⁻¹² mol COS per mol dry air). COS is taken up by the plants through their stomata, and its exchange is closely related to the stomatal conductance of vegetation¹⁰. However, as COS shares the same entrance pathway to the leaf with CO₂, a connection between biogenic COS uptake and GPP can be created¹¹. COS is destroyed at the chloroplast surface by the enzyme carbonic anhydrase (CA) in a hydrolysis reaction, and unlike CO₂, is not respired back to the atmosphere as a part of plant metabolism¹⁰. GPP has been estimated from COS fluxes on vegetated environments^12,13,14, but its potential has not been harnessed in human-influenced environments. Urban EC fluxes of COS have been studied before over a few weeks in Innsbruck¹⁵, where the main conclusion was that better information on anthropogenic sources is still needed to properly utilize COS as a proxy for GPP in this highly built source area. The same conclusion was obtained by two recent flask sampling studies conducted in Barcelona, Spain¹⁶ and Lutjewad, the Netherlands¹⁷. They observed notable influence from maritime and industrial sources of COS preventing making solid estimation of GPP.

In this study, we report the first EC fluxes of COS measured over a full growing season in Helsinki, Finland, in an urban area that also has a significant vegetated cover fraction (Figs. 1c, S1, and Table S1). This allows us to examine both biogenic and human-influenced trace gas fluxes in a setting that narrows the gap between the fully vegetated and the heavily built areas studied before. We study the impact of anthropogenic activities in the study area by comparing COS and CO₂ fluxes with carbon monoxide (CO) fluxes, which have been used as an indicator of anthropogenic emissions of CO₂ from combustion processes¹. We show how COS fluxes can be used to derive urban GPP using two different approaches and use it to calculate anthropogenic CO₂ emissions from NEE.

Carbon uptake of an urban green space inferred from carbonyl sulfide fluxes — **Fig. 1: Diurnal COS, CO, and CO₂ fluxes measured between May 12 and October 31, 2023 on a street and b vegetation sectors.**

Results and discussion

Trace gas fluxes during growing period

CO, COS, and CO₂ fluxes in street and vegetation sectors display notable deviations as a consequence of different surface cover fractions and human activities (Figs. 1 and S2). Both sectors function as sinks of COS reaching the highest hourly median uptakes of −10.6 and −19.7 pmol m⁻² s⁻¹, respectively. To compare, the mean daytime uptake of −23.5 pmol m⁻² s⁻¹ was observed in a deciduous forest during June, August, and September¹⁸, whereas the daily maximum uptake varied between −24 and −33 pmol m⁻² s⁻¹ during different years in a boreal coniferous forest¹⁹. When the sectors are examined together, a clear positive correlation between COS and CO₂ fluxes is observed, with an uptake ratio of 0.86 pmol μmol⁻¹ (R² = 0.39; Fig. S3a). When only times with simultaneous COS and CO₂ uptake are considered and placed on a similar scatter, the uptake ratio becomes 1.67 pmol μmol⁻¹ (R² = 0.52; not shown). This closely agrees with earlier reported values from leaf chamber measurements in a controlled greenhouse environment, where the ratio was 1.41 pmol μmol⁻¹ ¹¹. This shows the applicability for estimating GPP from COS fluxes at our site, since the methodology relies on the simultaneous uptake of both gases (Eq. (3)).

The street sector is a source of CO₂ with diurnal median values varying between 2.3 and 6.5 μmol m⁻² s⁻¹. The vegetation sector is on median a CO₂ sink between 8 a.m. and 5 p.m. reaching −6.6 μmol m⁻² s⁻¹, consistent with previously reported estimates (ca. −7.7 μmol m⁻² s⁻¹)²⁰. Nocturnal CO₂ sources are larger on the vegetation than the street sector likely due to soil and vegetation respiration. However, the daytime uptake in the vegetation sector offsets the nocturnal emissions, which is not the case in the street sector. When summed over a median day of the growing period, the vegetation sector sequestrates −8.0 gCO₂ m⁻² d⁻¹, comparable with −4.6 gCO₂ m⁻² d⁻¹ observed in Baltimore⁸, whereas the street sector emits 392.4 gCO₂ m⁻² d⁻¹. CO₂ and CO fluxes are also significantly correlated during daytime (R² = 0.74, p < 0.001, Fig. S3b) but not nocturnally. Strong correlation originates mainly from road transportation on the street sector, since there are no other combustion processes taking place in similar scales.

The street sector CO and CO₂ fluxes behave differently than corresponding fluxes in the vegetation sector because of transportation in the source area. The daily median CO source of 23.1 nmol m⁻² s⁻¹ originating from, on average 25,000 daily passing cars is comparable to the lowest observed CO fluxes in central London (16.9 nmol m⁻² s⁻¹)²¹. In the vegetation sector, the median daily emission is 7.5 nmol m⁻² s⁻¹, which still is higher than would be expected in a fully vegetated environment. A boreal forest emitted up to 1.6 nmol m⁻² s⁻¹ ²², and the highest monthly mean on a grazed grassland was 1.9 nmol m⁻² s⁻¹ ²³. Construction work on a tram line has taken place in the vegetation sector, which can explain large parts of the CO emissions. In addition, there may be some other unknown fossil fuel emissions in the vegetation sector such as local wood burning in the allotment garden or site machinery in the botanical garden. Also, another important access road 800–900 m from the tower, can influence the CO fluxes coming from the direction of the sector particularly at night-time when the atmosphere is stable and the source area extends longer. The impact is, however, not visible on CO₂ and COS fluxes due to the large mass of vegetation separating the road from the EC tower.

The EC measurement of COS flux in Innsbruck showed a day-time source, which was connected to exhaust fumes and tire wear of vehicular transportation¹⁵. A similar deduction was made in Beijing, where tire wear was conjectured the single largest source of COS during summertime²⁴. If an anthropogenic COS source originated from vehicular fuel combustion, a clearer relationship between COS and CO fluxes would have been seen, as is the case with CO₂. There is no statistically significant dependence between COS and CO fluxes (Fig. S3c) indicating mostly negligible anthropogenic COS emissions. Thus, our results do not support the earlier findings about COS emissions originating from tire wear. However, slight anthropogenic influence cannot be disregarded, particularly in the road sector causing some level of uncertainty in our analyses.

Novel estimation of urban GPP

During the brightest hours (photosynthetically active radiation PAR >700 μmol m⁻² s⁻¹), the leaf relative uptake (LRU, see the “Methods” section) needed to estimate GPP from COS flux had medians of 1.12 (interquartile range 1.0–1.3) and 1.45 (1.3–1.5) in the vegetation sector, as determined with PAR and CAP methods, respectively. These values compare well with 1.68 obtained for natural ecosystems in a review study²⁵. LRU_PAR smoothly decreases with PAR, whereas LRU_CAP saturates earlier by PAR and has a wider range of values on a single PAR due to the moisture conditions—namely vapor pressure deficit (VPD) and soil water content (SWC)—being taken into account (Fig. S4a).

The four methods used to estimate GPP (GPP_CAP and GPP_PAR based on COS measurements, GPP_LC based on a light-response curve, and GPP_EC based on carbon balance partitioning by respiration) provide a similar, qualitatively expected performance on the vegetation sector with the largest uptake in daytime and (near) zero at night-time (Fig. 2a). GPP_PAR yields the highest median biogenic uptake of 18.5 μmol m⁻² s⁻¹ whereas with other methods the peak median values remain between 11.7 and 14.6 μmol m⁻² s⁻¹. GPP_EC results in some slightly negative nocturnal GPP values as a consequence of uncertainty in ecosystem respiration (R) by the simple model used in this study. The estimated mean R (3.9 μmol m⁻² s⁻¹) agrees with the measurements conducted in Boston metropolitan area²⁶ [2.6–6.7 μmol m⁻² s⁻¹], but yield lower values compared to chamber measurements conducted in the vegetation sector in an earlier study²⁷ [5.5–6.1 μmol m⁻² s⁻¹]. In the latter, the chamber measurements were only made from lawns and meadows and thus did not present all soil and ground vegetation types within the vegetation sector.

**Fig. 2: Diurnal cycles of gross primary production (GPP) estimated with different methods on the street and vegetation sectors.**

The COS-based GPP estimations match well with GPP_EC and GPP_LC which are the more traditional methods to estimate GPP from EC measurements in vegetated ecosystems. GPP_LC is essentially a parameterization of GPP_EC as a function of PAR. Thus, the light response curve estimation of GPP can be used as a reference value for photosynthesis where there is a distinct and well-defined green sector. Also, GPP_LC works well against the small and occasional anthropogenic contributions visible in GPP_EC due to the averaging nature of parameterization. However, without the near-pure biogenic signal, GPP_LC cannot be parameterized, which becomes an essence of the NEE partitioning problem in urban areas.

GPP_CAP and GPP_PAR provide an independent mean to estimate GPP, but as both rely on COS concentration and flux measurements, they show more variability with similar peaks than the other two methods. GPP_PAR reaches higher peak values and shows steeper changes in both morning and evening hours, as PAR is considered the only limiting factor of LRU. On the contrary, GPP_CAP considers the environmental water availability as a part of the stomatal conductance model, which makes the slope more gentle during the transition periods of the day. This implies an insufficiency of GPP_PAR in the current ecosystem. High GPP values given by the method were noted already when the parameterization was used in a boreal forest site¹³ and in comparison with other methods at the same site¹⁴. High estimates are based on GPP_PAR being originally parameterized in optimal light conditions, which translates into unrealistically high GPP. Even though light conditions are less limited on a relatively open urban canopy compared to boreal forest, the method still overestimates. Nevertheless, it is used despite the different imperfections to provide the first COS-based GPP estimates.

Differences between methods are emphasized in the street sector (Fig. 2b), where GPP estimates are lower than in the vegetation sector. As expected, the pitfall of using traditional, CO₂-based partitioning of EC fluxes (GPP_EC) in a human-influenced context becomes apparent. Because the method only assumes a temperature-dependent R and GPP to play a role, it fails to recognize moments with negative GPP as anthropogenically influenced. Hence, it is not reasonable to use it as a reference for other models’ performance. The other methods yield qualitatively reasonable patterns for CO₂ uptake. The magnitude of the estimated GPP follows inversely the number of environmental variables used in each method: GPP_LC depends on PAR and yields a median GPP peak of 11.9 μmol m⁻² s⁻¹, GPP_PAR additionally depends on COS flux and ratio of CO₂ and COS molar fraction (({X}_{{{rm{CO}}}_{2}})/({X}_{{rm{COS}}})) resulting a peak value of 9.7 μmol m⁻² s⁻¹, and GPP_CAP with most environmental dependencies resulting a peak value of 8.8 μmol m⁻² s⁻¹. GPP_CAP shows an earlier morning increase due to a more flexible response to environmental variables. Both COS-based methods decrease earlier than GPP_LC in the afternoon, with GPP_CAP being 50% of GPP_LC between 11 a.m. and 5 p.m. This is partly caused by the diurnal cycle of COS flux (Fig. 1a) and partly by the variability of ({X}_{{{rm{CO}}}_{2}})/({X}_{{rm{COS}}}), which is approximately 10% lower in the afternoon than in the morning (Fig. S5c).

Uncertainties

The benefit of the COS-based methods is that real-time information on the plant uptake is obtained in the form of COS flux. This, however, assumes that the measured COS signal contains only the biogenic impact, which is an ideal case. Soil is also a known contributor to the ecosystem scale COS fluxes. Soil fluxes were not separately measured in this study, but have earlier been deemed to account for 10–20% of the ecosystem scale COS uptake in a boreal pine forest²⁸. Overall, soils with oxygen mostly function as moderate COS sinks, with the exceptions of deserts and some agricultural lands^25,29. Due to the small contribution of soils to net COS flux, we ignore it and consider it as an uncertainty.

For COS measurements made in a more densely built environment, a combination with modeling may be needed because the signal of biogenic uptake gets easily mixed with the anthropogenic signal. The possible traces of exhaustion fumes can dilute the biogenic signal, for which reason COS methodology is potentially jeopardized in cities. For example, a flask sampling over the San Francisco Bay Area concluded that improved GPP estimates are needed to distinguish urban biosphere signals³⁰, whereas another flask sampling study in Barcelona could distinguish a sink of COS in the urban forests, but not anymore in individual parks in the densely built parts of city¹⁶. Overall, for the COS-based methods to work in CO₂ flux partitioning, a sufficient amount of photosynthesizing biomass is needed in the flux source area. We show that on the street sector, which has a 45% vegetated land cover fraction, COS-based GPP yields sensible results. Still, this is not necessarily the lower limit for the minimum required vegetation for observing COS signals.

The path from COS flux to GPP is paved through LRU, which is directly related to stomatal conductance instead of GPP but is easier to utilize than a complex model for vegetative uptake of CO₂. Moreover, combining LRU with measurements is simpler than a model for stomatal conductance. LRU is not a rainmaker, however, as simplicity comes with a price. When studying our heterogeneous environment, it is not possible to consider the variability in species composition, light and moisture conditions, and soil properties, which are known to impact LRU^13,31. Instead, a heterogeneous environment forces us to make assumptions related to the urban environment overall. As it cannot be distinguished how different vegetation types impact the measured signal within and between the sectors, the fluxes contain the impact of diverse vegetation on the ecosystem level. This sets an unknown level of uncertainty in the analysis. LRU methodology will, however, be useful, because the street and the vegetation sectors experience different atmospheric mixing ratios of COS (Fig. S5), which is related to the GPP estimated using LRU. In this study, two parameterizations of LRU are used, both of which have been derived for a boreal forest site (see GPP methods). Even though using LRU_PAR and LRU_CAP is justified as LRU has been found to be relatively invariant within the boreal biome³², it is important to note that LRU values between species may vary notably³³. The LRU values we have obtained should be used with care in other urban areas as they are only representative of the boreal biome. A Monte Carlo-based uncertainty analysis conducted showed, however, that the accuracy of COS measurements is a greater source of uncertainty than the LRU parameterizations (see SI Uncertainty analysis).

The Kok effect, or the light-induced part of the respiration³⁴ has not been considered when parameterizing GPP_LC and R. The possible uncertainty caused by this has been studied using Monte Carlo simulation (see SI Uncertainty analysis), which shows that R estimate has most error around the lightest time of the year (Fig. S6e), which was also notably warm and dry in Helsinki. Thus, the uncertainty may derive from a low nocturnal data availability affecting parameterization, or R being impacted by the dry conditions. Over the measurement period, the cumulative uncertainty of R is 1.7%. To GPP_LC this is reflected as a 0.9% uncertainty, with similar behavior over the measurement period.

Residually solved anthropogenic emissions

The anthropogenic CO₂ fluxes (F_a) in the street sector obtained with CAP, PAR, and LC methods using Eq. (1) correlate with a bottom-up estimate of CO₂ emissions from traffic (({F}_{{{rm{CO}}}_{2,{rm{traffic}}}})) but show slightly lower emissions (Fig. 3). ({F}_{{{rm{CO}}}_{2,{rm{traffic}}}}) reaches a median of 10.2 μmol m⁻² s⁻¹ whereas the other methods range between 8.2 and 9.2 μmol m⁻² s⁻¹. An earlier modeling study reported a summer-time maximum traffic emission of 9.3 μmol m⁻² s⁻¹ ³⁵, which is close to our estimates. A notable feature of all methods is the underestimation of nocturnal emissions, which derives from uncertainty in the ecosystem scale respiration estimate. Difference between F_a’s and ({F}_{{{rm{CO}}}_{2,{rm{traffic}}}}) partly results from the different natures of methodologies compared. EC can only observe one limited footprint area at a time, whereas the bottom-up estimate contains the full emission without any going undetected or taken up by the vegetation on the way to the EC tower. In principle, ({F}_{{{rm{CO}}}_{2,{rm{traffic}}}}) assumes the full traffic signal to arrive at the EC setup every moment. F_a,LC is closest to the bottom-up estimates (R² = 0.83, Fig. 3), which is the only of the three methods showing the expected two peaks on F_a by morning and afternoon rush hours. F_a,LC shows, on average, 33% lower values when compared to ({F}_{{{rm{CO}}}_{2,{rm{traffic}}}}). A close fit confirms the assumption of similarly behaving vegetation between the two sectors since GPP_LC parameterized on the vegetation sector performs well on the street sector. Although the best results are obtained with GPP_LC, it is not reproducible in every urban setting, as a large vegetative mass without notable anthropogenic CO₂ emissions is required for its parameterization.

**Fig. 3: Estimates of the anthropogenic CO₂ fluxes (F_a) in the street sector.**

The COS-based CAP and PAR methods have R² values of 0.66 and 0.68, respectively. The lower GPP values during the afternoon hours (Fig. 2) when compared to GPP_LC translates into lower afternoon F_a as it is obtained as a residual from GPP and R. An additive part of the discrepancy can derive from the accumulation of error: Initial signal of high-frequency ({X}_{{rm{COS}}}) measurements has a lot of noise by default, which affects the quality of the flux calculated with the EC technique. The random errors of CO₂ fluxes can vary between 10–30%³⁶ but are even 35% for COS fluxes³⁷. Looking at the big picture, however, COS methods succeed qualitatively in producing diurnal dynamics of F_a and a relatively good correlation, which is encouraging. If F_a,LC is considered the desired output, then CAP and PAR both produce credible results, even though the daily sums of emissions for F_a,PAR and F_a,CAP are 24% and 21% lower than that of F_a,LC, respectively.

Long-term variability

All methods catch the variability of the anthropogenic (traffic in our case) CO₂ emissions and GPP during the measurement period (Fig. 4). ({F}_{{{rm{CO}}}_{2,{rm{traffic}}}}) in the street sector, it varies little over the measurement period, remaining between 6.9 and 8.4 μmol m⁻² s⁻¹. As with the diurnal variability, F_a obtained with different methods yields mostly lower estimates than obtained with the bottom-up approach. F_a,LC is, on average, the closest to ({F}_{{{rm{CO}}}_{2,{rm{traffic}}}}) (3.1–10.9 μmol m⁻² s⁻¹), while COS based methods yield mostly notably lower estimates (F_a,CAP: −1.1 to 10.3 μmol m⁻² s⁻¹, F_a,PAR: 0.6–9.6 μmol m⁻² s⁻¹). Performance of COS-based methods improves notably when the amount of available data from street sector increases. Part of F_a,LC’s success comes from the fact that parameterizations always ignore a significant amount of variability, which is detected in the COS flux-based methodology. However, the results encourage the use of light response curves where applicable.

**Fig. 4: Temporal evolution of the estimated anthropogenic CO₂ fluxes (F_a) and gross primary productivity (GPP) in the street and vegetation sectors using different methods.**

The seasonal dynamics of GPP (Fig. 4b) reflect variations in environmental conditions that the different methods are able to catch. After the driest and hottest period at the end of June (Fig. S7), there is a clear dip in the magnitude of GPP. The cloudy and rainy start of August shows a clear decrease in biogenic activity. During October, the vegetation prepares for winter dormancy, and the photosynthesis ceases completely. Finally, different methods converge towards each other: GPP approaches zero regardless of the method, thus F_a approaches R—NEE. The last week of the campaign shows an increase in all F_a’s without a significant increase in data availability. This suggests that as the temperatures fall closer to 0 °C, it becomes more likely that there are anthropogenic CO₂ emissions from also other than vehicular sources. GPP_LC, the most accurate on F_a, shows the least variability with the average observed CO₂ uptake of 7.9 μmol m⁻² s⁻¹. COS flux-based methods are, as expected, similar to each other, but GPP_PAR shows larger variability both between and within the weeks. GPP_CAP yields the lowest average CO₂ uptake, but a relatively high reactivity to the environmental conditions, shown as a higher standard deviation than GPP_LC.

In summary, we demonstrated that COS fluxes can be used to give realistic measurement-based estimates of urban ecosystem level GPP both on diurnal and season scales. The obtained GPP values can be used together with the estimation of ecosystem respiration to estimate anthropogenic emissions within the source area of the EC measurements. Compared to light-response curves COS-based methods need a lower fraction of green area and are not dependent on an NEE measurement of purely biogenic origin, thus being a better fit for the urban environment. Nonetheless, the light-response curve of GPP remains a useful and more accurate tool in the areas where a reasonable parameterization is possible. We also acknowledge that the COS methodology might not be applicable in environments with high anthropogenic influence. However, in the areas, where the fraction of vegetated areas is large, COS flux measurements can provide useful insights to estimate the magnitude of CO₂ uptake within the footprint.

Future research on urban COS exchange should consider conducting EC and chamber measurements using both shoot and soil chambers in urban vegetation to obtain a more detailed picture of the COS and CO₂ fluxes along the ecosystem scale. Furthermore, COS-based GPP methodologies should be compared with other methodologies, such as remote-sensed solar-induced chlorophyll fluorescence (SIF). By expanding the methodology to other urban areas also the global COS budget closure could be further enhanced.

Methods

Measurement setup

Eddy covariance (EC) measurements were conducted on top of a 31 m high measurement tower located at the SMEAR III (Station for Measuring Ecosystem–Atmosphere Relationships³⁸) in Helsinki, Finland (60°12’N, 24°58’E, 26 m above sea level). The station serves as an ICOS ecosystem associate site (FI-Kmp). The continuous measurement setup consisted of a uSonic-3 Scientific sonic anemometer (Metek GmbH, Elmshorn, Germany) to measure three-dimensional wind components and an enclosed path infrared gas analyzer (LI-7200RS, LI-COR, Lincoln, NE, USA), the standardized device for ICOS to measure CO₂ and water vapor molar fractions³⁹. These continuous measurements were complemented with an Aerodyne QCL gas analyzer (AD-QCL; Aerodyne Research Inc., Billerica, MA, USA) between 12 May and 31 October 2023 to measure the molar fractions of CO, COS, CO₂, and water vapor. Sample air was drawn to the base of the tower through a 40 m long PTFE tubing (8 mm i.d., 22 l min⁻¹), from where a sub-flow of 7.5 l min⁻¹ was guided to the instrument through 4 m long PTFE tubing (4 mm i.d.) All measurements were made at 10 Hz frequency. COS concentration was calibrated daily against the NOAA-2004 scale (474.2 ppt) every 24 h. The device’s drift was corrected by employing nitrogen as a background measurement every three hours. Auxiliary environmental measurements are described in Supporting Information (SI).

Flux processing

The vertical wind and trace gas molar fractions were utilized to compute 30-min average fluxes. The process involved despiking, linear detrending and 2-dimensional coordinate rotation, following standard EC processing approaches^40,41. The fluxes were computed utilizing the maximum covariance method where the time lag of CO₂ was used for COS due to the noisy COS signal³⁷. The obtained fluxes underwent spectral and storage corrections, which are described in SI. The co-spectra of COS with vertical wind exhibited a distinctive shape for the highest frequencies (Fig. S8), and the spectral correction of CO₂ was thus utilized. Storage flux below the measurement height was derived by assuming a uniform concentration change through the profile for each gas (Fig. S9)^37,42,43,44. To ensure the quality of the flux data, the following criteria were applied: flux stationarity <60%, kurtosis of the observation distribution between 1 and 8, and skewness between −2 and 2. Additionally, u_* filtering, with a threshold set at u_* = 0.19 m s⁻¹, was employed to eliminate the impact of low-turbulence situations⁴³. Quality control was passed by 37.9%, 59.6%, and 45.9% of COS, CO₂, and CO fluxes, respectively. The relatively high omission percentage for COS fluxes was anticipated, primarily attributed to a low signal-to-noise ratio resulting from the inherently low atmospheric molar fraction of COS. Previous studies in forest ecosystems have utilized 34%¹⁸ and 48%³⁷ of all COS flux data. The time series of fluxes that passed the quality filter are illustrated in Fig. S2. A comparison between AD-QCL and LI-7200 latent heat (LE) and CO₂ fluxes exhibited a good agreement (R² = 0.83 and R² = 0.69), with AD-QCL yielding 14% larger and 5.4% smaller flux values, respectively (Fig. S10). Data were not gap-filled due to the heterogeneous nature of the site, and as gap-filling can bring uncertainty to the analysis⁴⁵.

Ecosystem-scale urban CO₂ exchange

The footprint area of the EC setup was divided into three sectors (Fig. S1), of which street and vegetation were used in this analysis as the wind direction was seldom from the built sector. The vegetation sector had 80% green land cover, whereas the street sector had almost equal amounts of paved (41%) and vegetated (46%) surfaces (Table S1). The major difference between these two sectors is the amount of human activity. The vegetation sector houses a botanical garden, an allotment garden, and recreational green spaces, while one of the busiest access roads of Helsinki city center passes the street sector. Over the study period, the road had an average traffic count of 23,400 vehicles per day as measured by the City of Helsinki traffic counter located 350 m south of the EC tower.

The urban ecosystem- or local-scale net exchange of CO₂ (NEE, in μmol m⁻² s⁻¹) as measured using the EC technique can be described using a simplified equation

$${rm{NEE}}={F}_{{{a}}}+R-{rm{GPP}},$$

(1)

where R is the combined vegetation and soil respiration, GPP is the amount of photosynthetic uptake of CO₂, and F_a combines all the anthropogenic sources of CO₂ within the footprint area. R can be further divided into autotrophic and heterotrophic respirations, i.e., natural CO₂ release from plants and heterotrophic activity, such as soil microbial decomposition, and the F_a into emissions from human respiration, building heating, and transportation⁸. In the vicinity of SMEAR III, however, transportation is by far the largest anthropogenic CO₂ source, as building emissions take place elsewhere due to district heating, and human respiration is also modest compared to traffic³⁵. Thus, F_a is considered synonymous with traffic emissions, keeping in mind the consequent uncertainty. To separate F_a, which is commonly the interest of urban observations, from the other components, estimations for R and GPP are needed.

A commonly used practice is to estimate R using an exponential function on temperature:

$$R={R}_{{{C}}}{Q}_{10}^{{T}_{{{sa}}}/10},$$

(2)

where R_C is the base level of respiration, Q₁₀ describes the increase of R when temperature increases by 10 °C, and T_sa is the driving temperature of the respiration. Following¹⁴, a half-hourly average of 10 cm soil temperature from the botanical garden and 16 m air temperature from the EC tower was used. Parameters were obtained by fitting night-time (PAR < 10μmol m⁻² s⁻¹) NEE data from the vegetation sector (Fig. S11), which is a common practice when estimating R on vegetated ecosystems⁴⁶. More information about the parameterization is available in SI.

GPP methods

The photosynthetic carbon uptake of urban green areas was estimated using four different methods, with two relying on COS flux measurements. To estimate GPP from ecosystem-scale fluxes of COS (({F}_{{rm{COS}}})), a leaf relative uptake (LRU) of COS and CO₂ was used^12,14,47, as follows:

$${{rm{GPP}}}_{{rm{COS}}}=frac{{F}_{{rm{COS}}}}{{rm{LRU}}}frac{{X}_{{{rm{CO}}}_{2}}}{{X}_{{rm{COS}}}}$$

(3)

where ({X}_{{{rm{CO}}}_{2}}) and ({X}_{{rm{COS}}}) are molar fractions (shown in Fig. S12). In essence, LRU describes the ratio of the COS and CO₂ fluxes normalized with their molar fractions. Originally, LRU was considered as a constant^11,12, but later studies have shown the importance of the diurnal dynamics of LRU^13,14. Ideally, LRU is measured independently using leaf chamber measurements of COS and CO₂ to get a sturdy estimate for it. However, chamber measurements are often neither feasible nor representative, which presents a challenge, particularly in urban green areas with highly diverse plant species. We tested two different means to parameterize LRU on an ecosystem scale (see below).

GPP_PAR from COS flux and light response of LRU

An earlier study made an LRU parameterization based on chamber measurements in Hyytiälä forest station¹³. It represents the LRU of the top canopy of a boreal Pinus sylvestris forest as a function of PAR following

$${{rm{LRU}}}_{PAR}=frac{607.26,upmu ,text{mol},,{text{m}}^{-2}{text{s}}^{-1}}{{rm{PAR}}}+0.57.$$

(4)

An earlier study observed no significant differences between the LRU values of coniferous and broad-leaved tree species³¹. Furthermore, it has been shown that LRU is relatively invariant within the boreal biome³². Hence, the method is used here as an approximation for the diverse footprint area with predominantly broad-leaved trees and managed urban grasslands. LRU_PAR was used in (3) to obtain GPP_PAR in both the vegetation and street sectors.

GPP_CAP from COS flux and environmental parameterization

GPP_CAP is based on the CAP (carboxylation capacity) stomatal conductance optimization model^14,48. Besides PAR, it takes into account more environmental variables relevant for LRU, such as VPD, SWC, and leaf area index (LAI) following

$${{rm{LRU}}}_{{{CAP}}}=frac{1}{1.21}frac{{X}_{{{rm{CO}}}_{2}}}{{X}_{{{rm{CO}}}_{2}}-{Gamma }^{* }}left(1+sqrt{frac{{K}_{{{sl}}}| {Psi }_{{{c}}}| }{1.6{g}_{{rm{c}}}{rm{VPD}}}}sqrt{1+frac{2{Gamma }^{* }{g}_{{rm{c}}}}{alpha {rm{PAR}}}}right).$$

(5)

It is, in principle, universal, although applying it on different sites requires good availability of environmental parameters. The list of variables and parameters and their source is shown in Table S3. LRU_CAP is used in Eq. (3) to obtain GPP_CAP in both urban and street sectors.

GPP_LC from an ecosystem-scale light response curve

GPP_LC utilizes a form of saturating light response curve also originally used on forest ecosystems. The formulation was taken from a subarctic boreal forest as⁴⁶

$${{rm{GPP}}}_{{{LC}}}=frac{alpha {rm{PAR}}+{P}_{{{max}}}-sqrt{{(alpha {rm{PAR}}+{P}_{{{max}}})}^{2}-4theta {P}_{{{max}}}{rm{PAR}}}}{2theta }f({T}_{{{a}}}),$$

(6)

where α is the quantum yield, or the initial slope of the light response curve, I denotes PAR, P_max light-saturated rate of GPP, and θ is a curvature parameter. The temperature response of photosynthesis (f(T_a)) is taken into account as

$$f({T}_{{{a}}})=frac{1}{1+exp (2({T}_{0}-{T}_{{{a}}}))},$$

where T_a is air temperature at 16 m, and T₀ = −2 °C is the inflection point. Parameters were fitted as described in SI (Fig. S11). GPP_LC was then calculated for both vegetation and road sectors using the fitted parameters.

GPP_EC from traditional CO₂ flux partitioning

GPP_EC was employed in a “traditional” manner to distinguish carbon exchange components in vegetated ecosystems where it is estimated as a residual from NEE measured using EC and R(2), as follows:

$${{rm{GPP}}}_{{{EC}}}=R-{rm{NEE}}.$$

(7)

In this study, the method was primarily utilized for comparison to the other methods and secondarily to demonstrate its incompatibility in areas where anthropogenic CO₂ emissions become non-negligible.

Traffic emissions

To assess the accuracy of the final anthropogenic emissions obtained with different GPP estimates, we compare the flux-derived estimates against bottom-up estimates of fossil fuel emissions originating from vehicular transportation in the street sector (({F}_{{{rm{CO}}}_{2,{rm{traffic}}}})). Estimates of F_a were only made for the street sector because human activities in the vegetation sector were small. Also, we only consider F_a estimates just by LC, CAP, and PAR methods as for EC method F_a is trivially zero. The traffic rate measured at the access road by the City of Helsinki was combined with weighted unit emission factors (EF) obtained from The Handbook of Emission Factors for Road Transport (HBEFA)⁴⁹. EFs were obtained separately for different road types, each with their mean velocities matching with those obtained from the traffic counts. Velocity-dependent EF was obtained by fitting a line to the velocity-EF plane (Fig. S13b). The obtained relationship was

$${{EF}}=-0.87V+182.7,left[{text{gCO}}_{2},{text{km}}^{-1},{text{car}}^{-1}right]$$

(8)

where V is the average speed in 30-min period in km h⁻¹. The emission factor was multiplied by the number of cars per 30-min period and normalized by the area of paved land cover on the street sector to obtain the final vehicular CO₂ emission. The emission factors on the velocity range from 30 to 70 km h⁻¹ were considered trustworthy with this methodology. Earlier modeling from the area in 2012 estimated EF of 298 gCO₂ km⁻¹ car⁻¹ ³⁵, which is considerably higher than ours (183 ± 7 gCO₂ km⁻¹ car⁻¹). This can be partly accounted for the development of cars and the slowly increasing fraction of electronic vehicles and partly for the different methodologies used.

The real CO₂ signal originating from the street sector gets diluted on its path to the EC setup depending on the prevailing wind direction and the distance to the street. To account for this, an artificial dilution was added to the ({F}_{{{rm{CO}}}_{2,{rm{traffic}}}}) estimate. This was achieved by dividing the street sector into 20° slices with radii of 350 m (distance to the traffic counter, see Fig. S1), and weighting each estimate with a factor

$${W}_{{{slice}}}=frac{{p}_{{{slice}}}}{{p}_{{{slice,max}}}},$$

(9)

where p_slice is the paved fraction in each slice and p_slice,max is the highest paved fraction across all slices. Thus, ({F}_{{{rm{CO}}}_{2,{{traffic}}}}) was weighted for every timestep with a factor ranging between 0–1 depending on the average wind direction during the 30-min period.