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Estimation of greenhouse gas emission factors based on observed covariance of CO2, CH4, N2O and CO mole fractions



Covariances among major anthropogenic greenhouse gases were studied during three cold-air pool episodes in the Pannonian Basin to better constrain their emission factors for Europe.


On the base of observed covariance between carbon dioxide, methane, carbon monoxide and nitrous oxide atmospheric dry air mole fraction in a region of the Pannonian (Carpathian) Basin during three cold-air pool episodes in January–February 2017, emission factors relative to carbon dioxide were determined. For the determination of the emission of carbon dioxide, a simple boundary-layer budget model was compiled. The model gave 6.3 g m−2 day−1 carbon dioxide emission for the footprint area of the measurements on average for the period of the episodes. The 6.7–13.8 nmol μmol−1, 0.15–0.31 nmol μmol−1 and 15.0–25.8 nmol μmol−1 ratios for CH4:CO2, N2O:CO2 and CO:CO2, respectively, correspond to 15.3–31.7 mg m−2 day−1 methane, 0.9–2.0 mg m−2 day−1 nitrous oxide and 60.0–103.4 mg m−2 day−1 carbon monoxide emissions for the region. These values are somewhat higher than the officially reported bottom-up annual national averages for Hungary, which are explained by the winter conditions and intensive domestic heating.


The study indicated the high share of biomass burning in residential heating in rural environment that results in high carbon monoxide emission relative to that of carbon dioxide. It also indicated that the actual emission factor for nitrous oxide may exceed the range given in the guidelines for inventory compilation, which should be taken into account in reporting. It is shown that even a simple boundary-layer budget model might give realistic emission estimation under cool-air pool episodes.


Any change in the atmospheric budgets of greenhouse gases (GHGs), in the radiative forcing of the atmosphere causes global climate change. The drivers of the changing budgets are the natural and anthropogenic emissions, as well as the feedback processes generated by the climate change itself [1]. For the mitigation of climate change, we have to reduce the anthropogenic emission, if we want to avoid geoengineering. While the anthropogenic emission of carbon dioxide can be estimated with reasonable accuracy from fossil fuel usage and industrial statistics, the emissions of the other major greenhouse gases are known only with significant uncertainty [2]. Any contribution, which can improve the emission estimations, may help the better understanding of the greenhouse gas budget of the atmosphere and its processes, as well as it may help the elaboration of emission control strategies and the checking of their effectiveness. Emission inventory guidelines like [3] cannot exactly specify emission factors for each activity at each location that may distort the officially reported values, the essential input of the European Union’s emission control policy. It is highly desirable to check the suggested emission factors wherever it is possible. In this study, we take advantage of special meteorological situations formed in Central Europe to directly estimate emission factors for greenhouse gases.

There are two main types of methods for the determination of emission. The so-called “bottom-up” approach obtains regional, national or global emissions by multiplying statistical activity data with the appropriate emission factors determined empirically for typical sources, while the so-called “top-down” methods are based on atmospheric concentration measurements [4]. Based on atmospheric concentration measurements, the inverse atmospheric transport models can determine the spatial distribution of the intensity of emission (see e.g., [5,6,7,8]), while the boundary-layer budget (BLB) methods can estimate the emission of a region [9, 10]. The boundary-layer budget models can be applied from a single night to a several-days-long episode (see e.g., [11,12,13,14,15,16]).

The sources of greenhouse gases partly overlap. The ratios of their emissions are characteristic for the source. These substances are rather inert chemically, the atmospheric transport affects them uniformly, and therefore, their ratios do not change during the transport time. As a result, the correlation between their concentrations at a monitoring site gives information on the sources. If the emission of any of the substances is known then that of the others can be calculated from the relationship. The correlation method belongs to the “top-down” ones, and it has been widely used for a long time (see e.g., [17,18,19,20,21,22,23,24,25]). This method is especially applicable for the estimation of the anthropogenic emission in wintertime when the biological activity and photochemical production providing the natural sources of the major anthropogenically influenced greenhouse gases are low.

During winter high-pressure situation, cold air may pile up in the bottom of topographic basins due to the typically low wind speed and the radiative cooling of the surface characterizing such a meteorological situation. The resulted stable atmospheric stratification may persist for several days when it is called a cold-air pool episode [26]. During such an episode, pollutants emitted at the surface accumulate in the shallow boundary layer due to the limited atmospheric mixing. The rate of the accumulation may be used to estimate their emission. The cold-air pool episodes and their remarkable effect on the local/regional air quality are widely studied in the geographically exposed regions of the world, especially in the Intermountain West region of the United States (see e.g., [26,27,28,29,30,31,32,33,34,35,36]).

Hungary is located in the Pannonian (Carpathian) Basin surrounded by the Carpathian Mountains and by the eastern part of the Alps including the northern Dinaric Alps. These surrounding mountains rise 1000–2000 m above the bottom of the basin, the Pannonian Plain. Taking advantage of three cold-air pool episodes formed in the Pannonian Basin in January–February 2017, and the concentration measurements at the greenhouse gas monitoring station of the Hungarian Meteorological Service, we have estimated the relative emission factors of carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O) and carbon monoxide (CO) based on the observed covariance of CO2, CH4, N2O and CO dry air mole fractions. The values obtained are characteristic for the region and for winter conditions, and they can be incorporated into the emission inventories with these constraints. We have also attempted to estimate the absolute emission by means of a simple boundary-layer budget model.

Although carbon monoxide is only a weak greenhouse gas on its own, but influencing the methane content of the atmosphere through chemical reactions, it is often called as “indirect” greenhouse gas. For simplicity, in this paper, we will also use the term “greenhouse gas” or “GHG” for carbon monoxide. Also for simplicity, we use the term “concentration” for the atmospheric dry air mole fraction actually measured.

Measurements and methods

Greenhouse gas concentration measurements

Hegyhátsál tall-tower greenhouse gas monitoring station of the Hungarian Meteorological Service is located in the western part of the Pannonian Plain (46º57′ N, 16º39′ E, 248 m a.s.l.—Fig. 1) where a TV/radio-transmitter tower owned by Antenna Hungária Corporation is equipped with meteorological sensors and gas analyzers. The monitoring site is located in a fairly flat region, which does not modify the large-scale atmospheric conditions significantly. The prevailing wind directions are the northerly and the southerly ones due to the Alps west of the station. Human habitations in the region of the tower are only small villages (100–400 inhabitants). The nearest one is the single-street village Hegyhátsál, giving the name to the monitoring site, which is located 500–1200 m to the northwest and has only 157 inhabitants. The nearest city is Körmend (11,305 inhabitants), 7 km to the northwest. Larger cities of the region are Zalaegerszeg (58,154 inhabitants, 20 km to the southeast) and Szombathely (78,025 inhabitants, 30 km to the north). The numbers of inhabitants are reported by the Hungarian Central Statistical Office for 1 January 2017 [37]. Local roads carry only low traffic, 300–700 vehicles per day [38]. There is no notable industrial activity in this dominantly agricultural region.

Fig. 1
figure 1

Location of the monitoring site, the approximate contour of the Pannonian (Carpathian) Basin (solid line) and the Pannonian Plain (dashed line) on Google Earth

At Hegyhátsál tall-tower monitoring site carbon dioxide concentration has been continuously monitored at four elevations (10 m, 48 m, 82 m and 115 m above the ground) since 1994, using non-dispersive infrared gas analyzers (during the period studied here: Model LI-7000, Li-Cor Inc., Lincoln, Nebraska, USA). The analyzer was calibrated against four whole air (CO2-in-natural-air) standards produced and certified by the Central Calibration Laboratory of the World Meteorological Organization [39]. Carbon dioxide concentration was also measured along with that of methane at 82 m elevation using a Picarro Model G2301 cavity ring-down laser spectrometer (Picarro Inc., Santa Clara, California, USA). At the same elevation nitrous oxide and carbon monoxide concentrations were also monitored by a Model 913-0014 Enhanced Performance N2O/CO analyzer (Los Gatos Research Ltd., San Jose, California, USA). For CH4, N2O and CO measurements the analyzers were calibrated against four whole air standards produced and certified by Max Planck Institute for Biogeochemistry, Jena, Germany. These standards are also traceable to the WMO primary standards. Hegyhátsál tall-tower GHG monitoring site is a member of the Global Atmosphere Watch program of WMO [40] and a member of the Cooperative Global Air Sampling Network operated by the United States National Oceanic and Atmospheric Administration (NOAA, USA) Earth System Research Laboratory [41]. The station identification code of Hegyhátsál is HUN in both networks.

In addition to the in situ measurements, a pair of flask air samples are taken for NOAA for greenhouse gas measurements every week in the early afternoon hours when the atmospheric mixing is the most intensive. Comparison of the in situ measurements with the flask sample analyses is an integral part of the quality assurance protocol of the station. The surface–atmosphere exchange of CO2, N2O and CO is also measured at the site using the eddy covariance method. The sensors are located at 82 m above the ground providing more extended spatial representativeness than the more common low elevation (few meters above the ground) systems. A detailed description of the site, monitoring program, source area characterization and instrumentation can be found in [42,43,44,45,46].

Meteorological data

For the characterization of the weather conditions at the monitoring site, the ERA5 reanalysis dataset of the European Centre for Medium-Range Weather Forecasts [47] was used. Vertical profile of temperature, relative humidity, wind speed and geopotential up to 700 hPa, as well as boundary-layer height, precipitation amount and surface pressure data were downloaded for the grid-point nearest to the monitoring site and for the eight surrounding grid-points (see Fig. 2) with a 0.25° spatial and 1 h temporal resolutions for January–February 2017.

Fig. 2
figure 2

Location of the monitoring site and the grid-points for which meteorological data from ERA5 dataset were used in the study

For the identification of the air masses arriving at the monitoring site, the Hybrid-Single Particle Lagrangian Integrated Trajectory (HYSPLIT) Model [48] developed by the US National Oceanic and Atmospheric Administration’s Air Resources Laboratory [49] was applied. 3-Dimensional backward trajectories were calculated to trace the air masses back in time for 24 h. The model was fed by the Global Data Assimilation System (GDAS) dataset [50] providing 0.5° spatial and 3-h temporal resolution.

Selection of the cold-air pool episodes

The scientific literature is rich in indexes for the identification of stagnant weather conditions favorable for the accumulation of air pollutants (see e.g., [31, 51,52,53,54,55,56,57]—and references therein). These indexes comprised different meteorological variables to describe the reduced dispersion processes. The set of identification criteria may include maximum values for wind speed at different elevations, boundary-layer height, ventilation coefficient (integral of the wind speed from the surface to the top of the boundary layer), convective available potential energy, precipitation amount, etc. There is also a criterion on the minimum length of the stagnant period for being considered as an episode. However, there is no universally applicable stagnation index and set of criteria. The best set depends on the properties of the substance studied (e.g., ozone, particular matter, haze, etc.), and it may also depend on the geographical location and season. The threshold values applied as criteria are arbitrary, but supported by previous statistical or phenomenological studies.

Based on previous works [58], in the identification of the cold-air pool episodes, we primarily relied on the value of the boundary layer’s convective potential energy usually referred to as shallow convective potential energy (SCP). SCP is formally similar to the convective available potential energy [59], commonly abbreviated as CAPE, but the upper boundary of the integration is fixed at 850 hPa because typically the top of a cold-air pool remains below this level:

$${\text{SCP}} = - R_{d} \mathop \int\limits_{{p_{0} }}^{{850 {\text{hPa}}}} \left( {T_{\text{vp}} - T_{\text{ve}} } \right){\text{dlnp}},$$

where Rd is the specific gas constant of dry air, p0 is the surface pressure, while Tvp and Tve designate the virtual potential temperatures of the lifted air parcel and that of the environment, respectively. In order to be consistent with the phenomenologically observed cold-air pool episodes, the arbitrarily chosen maximum allowable SCP, ventilation coefficient and surface (10 m) wind speed values for being qualified a day as a stagnation day were – 250 J/kg, 3000 m2/s, and 3 m/s, respectively. We allow only traces of precipitation (< 0.5 mm/day) around the monitoring site during a stagnation episode.

Figure 3 shows the temporal variations of the key meteorological parameters used for the determination of the cold-air pool episodes, and that of a few others characterizing them, for the period of January–February 2017. After the cold front passed over the Pannonian Basin on 14 January, a stable high-pressure system started developing over Central Europe. By 20 January, it already covered a huge area from the British Islands to the Black Sea with its center in or close to the Pannonian Basin causing gradual cooling in the basin. The system slowly moved to the east, and fresh air entered into the basin from the north at its edge on 24–26 January. The restrengthened high-pressure system left the region only at the end of January when a small cyclone formed over Western Europe pushed it away to the east. After changeable weather in early February, another persistent high-pressure system developed over Scandinavia and started stretching to the south, over the Pannonian Basin. The cold air accumulated in the basin during this period was swept away by a cold front crossing the region on 17 February.

Fig. 3
figure 3

Temporal variation of SCP (a), ventilation coefficient (b), hourly precipitation amount (c), boundary-layer height (d) and sea level pressure (e) averaged over the 9 grid-points covered by the study (see Fig. 2), as well as the cold-air pool episodes (gray shaded periods)

Figure 3 indicates three cold-air pool episodes (19–24 January, 26–31 January, 11–17 February). The notable meteorological differences among these episodes are in temperature and cloudiness. The second half of January 2017 was unusually cold due to the long-lasting anticyclonic conditions. The daily maximum temperature was always below the freezing point and the minimums were as low as − 10 °C. On the contrary, during the episode in February the daily maximum temperature gradually increased up to + 10 °C, while the minimums did not go below − 4 °C. The radiative cooling was largely balanced by the increasing insolation. The episode at the end of January was heavily foggy, while the other two episodes were mostly clear.

During most of the cold-air pool episodes, air arrived at the monitoring station from the south sector (from southeast to southwest). The only exceptions were the first one and a half days of the first episode in January (19–20 January) and the first day of the episode in February (10 February). Although pollution accumulates all over the basin during stagnation, its distribution is not perfectly uniform due to the weak horizontal mixing. For getting a clearer picture of the emission, we selected only those periods of the cold-air pool episodes when the air arrived from the south sector (20–23 January, 26–31 January, 11–17 February).

Determination of the relative emission factors and the absolute emissions

As the sources of greenhouse gases may partly overlap, the relationship between their emissions can characterize the source or the combination of the sources. The atmospheric transport, dispersion affects the concentration of these chemically inert gases uniformly. The correlation between their concentrations at a monitoring site gives information on the sources. If the emission of any of the substances is known, then that of the others can be calculated from the relationship. However, the correlation method can only provide relative emissions.

We have also attempted to determine the absolute emission, at least on a qualitative level, using a simple boundary-layer budget model. It also checks if such a simple model could provide realistic results under a cold-air pool episode. In this model, three vertically aligned boxes of a unit base area represent the atmosphere: boundary layer, residual layer and the free troposphere (Fig. 4). The height of the lowest box varies with that of the planetary boundary layer. The middle box represents the residual layer. Its height is supposed to be equal with the maximum height of the boundary layer on the previous day and the initial concentration in this box corresponds to that in the boundary layer at the time of the maximum height. The height of this box and the concentration in it are reset every day when the boundary-layer height reaches its daily maximum. The upper box represents the free troposphere where the concentration is permanently equal with the continental background one. The residual layer is not totally decoupled from the free troposphere. For the simulation of the dilution of the residual layer, its certain portion is replaced with free tropospheric air in each time step. The real vertical exchange of air could only be simulated in a one-dimensional model including the turbulent vertical exchange processes. Assuming a realistic range of 2–4% h−1, we tested the sensitivity of the model to this parameter. The calculated emission varied ± 16% relative to the average in this range. It is not critical besides the other sources of uncertainties with special attention to the neglected variable advection. In the model run presented in this study constant 3% h−1 exchange rate between the residual layer and the free troposphere containing background air was used.

Fig. 4
figure 4

Structure of the boundary-layer budget model

The mass balance in a box means that the concentration is driven by the combined effect of the mass leaving and entering the box, while the volume of the box is also changing (see [11, 60, 61]—and references therein). The boundary-layer box receives mass from surface emission and from the residual layer when the height of the boundary-layer is increasing. If the boundary-layer height exceeds the height of the residual layer, the boundary-layer box incorporates mass from the box representing the free troposphere. A part of the mass in the boundary-layer is transferred into the residual layer when the boundary-layer is shrinking, which modifies the concentration in the residual layer. The mixing within both boxes is assumed instantaneous. The concentration in the box representing the free troposphere is kept constant (background concentration).

The surface emission can be calculated so that it maintains the measured concentration change in each time step (1 h). The measurement level on the tower at 82 m above the ground, where all the GHGs are measured, is often above the nighttime boundary-layer, decoupled from the surface, and so the concentration data measured there are not suitable for emission calculations. For the emission estimation, the CO2 concentration data measured at 10 m above the ground can only be used. This monitoring level was always within the boundary layer. The footprint of the measurements depends on their height above the ground. Therefore, the CO2 emission calculated on the base of the measurements performed at 10 m above the ground does not fit perfectly into the emission relations determined for the elevation of 82 m, however, the technical and meteorological constraints do not make a more appropriate solution possible. For background concentration, 410 µmol mol−1 was set in the model. In January–February 2017, the minimum hourly concentration was 410.94 µmol mol−1 at the top of the tower (115 m above the ground), and still it was supposed to be an overestimation of the actual continental background concentration.

Results and discussion

Correlation between the GHG concentrations

Carbon dioxide, methane, nitrous oxide and carbon monoxide have long atmospheric residence time, and so, they undergo the same dispersion and long-range transport. Therefore, the fluctuation of the concentration at a given site is dominated by the emission in the footprint area of the measurements. A high correlation between the concentrations of these gases indicates a common source or a given combination of sources. The slope of the regression line reflects the ratio of their emission strength. Consequently, if the emission of one of the gases is known with reasonable confidence then that of the others can be calculated. Such a “top-down” atmospheric method has already been used for different substances in different parts of the world [19,20,21, 23].

Figure 5 shows the correlations between the gases studied. The parameters of the regression lines and the correlation coefficients are listed in Table 1. All correlation coefficients are statistically significant at higher than the 99% confidence level.

Fig. 5
figure 5

Covariance between CO2, CH4, CO and N2O concentrations during the episodes

Table 1 Parameter values of the regression lines ([x] = a[CO2] + b), the coefficients of determination (R2) between CO2 concentration and the concentration of the other substances measured, as well as the ratio of their standard deviations

Figure 5 and Table 1 indicate different emission regimes in the three periods studied: high ratios to CO2 in the first period (20–23 Jan), the same CO:CO2 ratio but lower ratios for the other two gases in the second (26–31 Jan), and reduced CO:CO2 ratio but increased N2O:CO2 ratio relative to the previous episode during the last episode (11–17 Feb). Several authors have already reported CO:CO2 and CH4:CO2 ratios from different parts of the world. For N2O:CO2 ratio less numerous data are available. The ratios in Table 2 have been selected to reflect the winter season or at least the non-summer one for higher comparability with our measurement results. However, the different climate of the monitoring sites may explain certain differences, and during the period covered by the measurements, there were significant technological developments at certain source categories (see e.g., the evolution of the vehicle exhaust regulations in [62]). Yet, our data fit into the above ranges or they are close to them.

Table 2 CH4:CO2, CO:CO2 and N2O:CO2 ratios measured in the different parts of the world during non-summer seasons

The high CO:CO2 ratio characterizing the two episodes in January indicates ineffective burning. The relatively high emission of carbon monoxide may originate from domestic heating. This hypothesis is also supported by the temporal variation of emission. In the case of constant emission, the concentration and the boundary-layer height are anticorrelated. The increasing boundary-layer height helps the dilution of the emitted substances reducing the concentrations, while as soon as the boundary-layer height is decreasing the emission starts increasing the concentrations in it. However, this phenomenon cannot be observed during the episodes in January (r = 0.18 and r = − 0.02, respectively), which suggests a covariance between the emission and the boundary-layer height keeping the concentration virtually independent of the boundary-layer height. In the villages in the region of the monitoring site mostly manually fed traditional, coal- or wood-burning heating appliances are used, although natural gas is also available. People ignite the stoves in the morning and leave them to cool down by the evening resulting in a dominantly morning, noon-time emission. The high CH4:CO2 and N2O:CO2 ratios suggest the dominance of biomass burning. Δ14CO2 measurements also indicate the high ratio of “modern” carbon in the excess CO2 in winter [70]. N2O:CO2 ratio in the first episode in January, and also in February, is above the upper limit calculated from the IPCC 2006 Emission Guideline [3] for wood/wood waste burning in the residential combustion category (0.15 nmol mol−1; upper value for N2O emission: 15 kg TJ−1 [0.341 kmol TJ−1]; lower value for CO2 emission: 95,000 kg TJ−1 [2159 kmol TJ−1]). The high N2O:CO2 ratio may also indicate a contribution from the transport sector, however, the traffic in the region is generally low. This result may have implication in the compilation of the national emission inventory report.

Domestic heating might not play such a dominant role during the episode in February when the temperature was significantly higher. The correlation coefficient between the boundary-layer height and the CO2 concentration at 10 m elevation was − 0.58, as it is expected in the case of a temporarily more even emission, and the CO:CO2 ratio was also lower.

Estimation of the emission

The boundary-layer budget model could only be used for the determination of the carbon dioxide emission because the other gases were measured only at such a high elevation (82 m above the ground) that was above the boundary layer during several nights. The box-model described in “Determination of the relative emission factors and the absolute emissions” section driven by ERA5 boundary-layer height data systematically gave negative emission for 2–4 h after the time of the maximum height. It was the consequence of the decreasing boundary-layer height, while the concentration measured in it was stagnant or still decreasing. It seems that the boundary-layer calculated for ERA5 collapses too early for the given meteorological situations. To overcome this artifact the boundary-layer height was fixed for 3 h after reaching its maximum height. This arbitrary solution largely eliminated the temporary negative emission and resulted in realistic overall emission values. A simple box model can only aspire to provide a qualitative emission estimation. In addition to the arbitrary solution, the advection not considered by the model also contributes to the uncertainty. The calculated CO2 emissions are 5.3 ± 3.1 g m−2 day−1, 8.3 ± 10.8 g m−2 day−1, and 8.4 ± 4.9 g m−2 day−1 for the three episodes, respectively. Uncertainty is given as the standard deviation of the calculated daily emissions during an episode. Emission values are expressed here and throughout the paper in mass of CO2, CH4, N2O, and CO, respectively.

For Hungary, covering the significant portion of the Pannonian Plain, only annual national anthropogenic CO2 emission data compiled following the IPCC Guideline [3] are available. Emission data at finer spatial and temporal resolutions are not available yet. The reported annual national anthropogenic CO2 emission for 2017 was 49,646 Gg [71]. It gives 1.46 g m−2 day−1 for the territory of the country on average. While the intensity of several sources does not show remarkable seasonal variation, the emission of commercial, institutional and residential heating, including biomass burning, responsible for 19,163 Gg in 2017 (0.56 g m−2 day−1) is concentrated for the winter season. Assuming that 2/3 of this emission are released into the atmosphere during the coldest 2 months, January and February (12,775 Gg during 59 days, equivalent to 2.33 g m−2 day−1), we can estimate (1.46–0.56) + 2.33 = 3.23 m−2 day−1 anthropogenic emission for these months as a nationwide average. Hegyhátsál tall-tower GHG monitoring station is also the place of continuous surface–atmosphere CO2 exchange measurements characterizing the net ecosystem exchange of the neighboring, dominantly agricultural region with forest patches [42]. This measurement indicates 2.00 g m−2 day−1 net release from the biosphere on average for January–February, 2017. Although the footprint of the flux measurements is only of the order of 10 km2, much smaller than that assumed for the concentration measurements, the resulted value may be valid for an extended region having the same land cover. Adding up these terms, we can estimate 5.23 g m−2 day−1 CO2 emission for an average winter day for Hungary, which is fairly close to the model result based on a few, actually measured days. Of course, we must not forget that the anthropogenic and biospheric emissions are not evenly distributed over the country and the uncertainty of the model results is high.

The CO2 emission values calculated by the model for the three episodes show neither systematic nor significant differences. Taking into account the notable differences in the uncertainty in the calculated emissions for the episodes, for the calculation of the average emission the inverse-variance weighting method was applied. Accepting the average CO2 emission calculated in this way (6.30 g m−2 day−1) and using the measured GHG to CO2 ratios the emission ranges for CH4, N2O and CO can be estimated for the given geographical region and environmental conditions. The inferred emission ranges for CH4, N2O and CO are 15.3–31.7 mg m−2 day−1, 0.9–2.0 mg m−2 day−1, 60.0–103.4 mg m−2 day−1, respectively. The natural sources, including the anthropogenically enhanced natural processes, of CH4, N2O and CO are presumably low during wintertime when the biological activity is limited by the low temperature. The concentration of the photochemically produced hydroxyl radical is presumably low and so the chemical reactions may not play a significant role in the formation of the GHG concentrations. Therefore, these values should only be compared to the bottom-up anthropogenic emission estimations. The average annual anthropogenic emission of CH4, N2O and CO for a unit area of Hungary in 2017 was 8.9 mg m−2 day−1, 0.46 mg m−2 day−1 and 13 mg m−2 day−1, respectively. Taking into account that both the emission data calculated by means of the boundary-layer budget model and those from the bottom-up approach carry high uncertainty, and the bottom-up approach gives annual average nationwide emissions, while the BLB model was applied for a few cold winter days when the heating emission might be extremely high, and for a specific region, the differences do not necessarily mean that the nationwide annual averages are underestimated. However, the significant differences justify further studies.

Two questions have remained open: (1) why was the CH4:CO2 ratio two times higher in the first episode of January than during the other two episodes, and (2) why did the N2O:CO2 ratio varied virtually independently from the other ratios? In the stagnant weather conditions characterizing the episodes studied, the combination of the trajectories with the gridded emissions from the EDGAR 4.3.2 database [72] has not revealed any characteristic features explaining the observed differences. Were the ratios measured influenced by some sort of episodic emission? Detailed footprint and source apportionment analyses may give the answer in the future, especially if activity data of reasonable temporal and spatial resolution are available.


Taking advantage of cold-air pool episodes in the Pannonian Basin, the ratio of carbon dioxide, methane, nitrous oxide and carbon monoxide emissions were determined giving relative emission factors for these substances. The concentrations show high (r > 0.88) correlations indicating a given source or combination of sources during each episode. However, the ratios between the emission strength of GHGs studied varied from episode to episode that could only be partially interpreted on the basis of the available data and modeling tools. We also proved that a simple boundary-layer budget model may be capable of providing realistic emission estimation under these special meteorological conditions, although the uncertainty of the model results is obviously high.

Availability of data and materials

Meteorological data used in the study were downloaded from the European Centre for Medium-Range Weather Forecasts where they are publicly available (!/dataset/reanalysis-era5-land?tab=overview). Carbon dioxide data are publicly available from the World Meteorological Organization World Data Centre for Greenhouse Gases ( Methane, nitrous oxide and carbon monoxide concentration data are available from the corresponding author on request.


CO2 :

carbon dioxide

CH4 :



nitrous oxide


carbon monoxide


greenhouse gas


boundary-layer budget


World Meteorological Organization


World Meteorological Organization Central Calibration Laboratory


Global Atmosphere Watch


National Oceanic and Atmospheric Administration


Hybrid-Single Particle Lagrangian Integrated Trajectory


Global Data Assimilation System


shallow convective potential energy


convective available potential energy


Intergovernmental Panel on Climate Change


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The authors gratefully acknowledge the NOAA Air Resources Laboratory for the provision of the HYSPLIT transport and dispersion model website ( used in this publication. The authors also thank Ákos Horváth, István Ihász, Gábor Kis-Kovács and Klára Tarczay (Hungarian Meteorological Service) for the valuable discussions on emission inventories, data retrieval and boundary-layer dynamics.


The study was supported by the Hungarian National Research, Development and Innovation Office (K129118), while the measurements were partially sponsored by the National Development Agency (OTKA K109764). Z. Barcza’s contribution was partially supported by grant EVA4.0 (CZ.02.1.01/0.0/0.0/16_019/0000803) financed by OP RDE.

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Concept of the study and writing of the manuscript: LH; trajectory evaluation: ZF; biosphere–atmosphere exchange calculations and critical revision of the manuscript: ZB. All authors read and approved the final manuscript.

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Correspondence to László Haszpra.

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Haszpra, L., Ferenczi, Z. & Barcza, Z. Estimation of greenhouse gas emission factors based on observed covariance of CO2, CH4, N2O and CO mole fractions. Environ Sci Eur 31, 95 (2019).

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