## Introduction

Climate change is considered to be one of the consequences of increased emissions of anthropogenic greenhouse gases during the industrial era, and carbon dioxide (CO2) is the dominant contributor to the enhanced radiative forcing caused by anthropogenic long-lived greenhouse gases. Atmospheric CO2 mole fraction has increased from ~280 ppm (parts per million) in 17501 to > 400 ppm in recent years2 due to the rapid growth of human activities and population since the beginning of the industrial era. About half of the anthropogenic CO2 emissions related to fossil fuel combustion and human driven land-use change is taken up by the ocean and the terrestrial biosphere3,4. In a top-down approach using atmospheric transport models, the global fossil fuel CO2 emissions have often been presumed to provide good estimates of the strength of the land and ocean sinks5. But recent studies suggest that uncertainties in fossil fuel emission database could lead to significant biases in the optimized estimates of biospheric flux6,7. In fact, uncertainties of fossil fuel CO2 emission estimates are growing because of increasing contributions from developing countries3,4,8,9.

About 70% of the current anthropogenic CO2 emissions is considered to come from urban areas that contain over 50% of the world population10, and thus accurate quantification of CO2 emissions from urban areas is of particular importance. The existing and projected rate of urbanization is different for different parts of the world; many cities in Asia and Africa are expected to continue to see rapid growths in population while cities in developed countries have basically already stabilized11. For effective mitigation actions against climate change, various independent approaches must be used to reduce the uncertainties associated with citywide greenhouse gas emissions estimates, and one of those approaches can be provided by atmospheric CO2 observations12. For this purpose, atmospheric CO2 measurements focusing on urban areas have been examined in recent years by means of citywide in-situ ground measurement networks13,14,15,16 or satellite measurements17,18. The former methodology provides dense and accurate data and the latter broad spatial coverage, whilst both also have limitations.

Since 2000s, atmospheric observation instruments onboard commercial airliners have successfully acquired extensive number of trace gas (including CO2) data19,20,21. The CONTRAIL (Comprehensive Observation Network for TRace gases by AIrLiners) program, an ongoing project that measures atmospheric CO2 and other trace gases using aircraft of Japan Airlines20, has obtained thousands of vertical profiles of CO2 over many airports since 200522,23,24,25. Given that major airports are often located reasonably close to large cities and airlines optimize their flight destinations with priority on connecting between large cities, data collected by commercial airliners might provide useful information that can contribute to better assessments of greenhouse gas emissions from cities, complementing ground and satellite measurements. Here we present some statistical results from analysis of urban CO2 emission signals contained in vertical profiles of atmospheric CO2 data over airports. We present detailed analysis of data obtained at Moscow, Tokyo and 34 other airports, to offer a conceptual framework in which urban emission estimates can be obtained consistently with the statistical properties of the measurements. We show that the magnitude of atmospheric CO2 variability increases with intensity of CO2 emissions from the neighboring cities, demonstrating the usefulness of commercial aircraft-based measurements for urban emission studies.

## Results

### Moscow

We analyzed appearance of high CO2 events in two altitude layers (4.0–4.5 km and 1.0–1.5 km) over Moscow Domodedovo Airport (DME) as a function of wind direction and speed (Fig. 1a,b). These plots indicate wind direction and speed in which high CO2 events were observed in the measurement area. At altitudes of 4.0–4.5 km, almost no CO2 enhancements in any wind direction and speed are evident (Fig. 1a), indicating that variability of CO2 enhancement (defined as excess CO2; see Methods) is small in the free troposphere. In contrast, at 1.0–1.5 km, it is seen that high CO2 events were associated with winds mainly from the northwest sector (Fig. 1b). At altitudes of < 2 km, our measurement aircraft was primarily in the southeast of the Moscow metropolitan area (pink area in Fig. 1d) in all cases and influenced by CO2 emissions from the city when advected from northwest. In addition, the fact that high CO2 events appeared with relatively low wind speed (<15 m s−1) suggests that a presence of strong emissions close to the airport is likely. The Moscow metropolis covers an area of ~50 km in the northwest-southeast direction, a distance an air parcel with a speed of ~15 m s−1 traverses in ~1 hour. Longer residence time of an air mass over the metropolitan area would allow city emissions to be more integrated into the air mass, leading to results consistent with the observations of high excess CO2 at low wind speeds. Histograms of excess CO2 values at both altitudes (Fig. 1c) shows that the excess CO2 at the lower altitude undergoes higher variability (i.e. larger spread of the histogram), and it is likely that the urban plumes contributed to the increased CO2 variability with decreasing altitude.

### Tokyo

Similarly, we analyzed the data over Tokyo Narita Airport (NRT), located ~60 km to the east of the Tokyo agglomeration center (Fig. 2). The flight tracks at <2 km altitudes over NRT are roughly located on the eastern edge of the metropolitan area (Fig. 2d). We found that high CO2 air masses were associated primarily with air parcels with relatively weak wind speed from the west of the measurement positions (Fig. 2b). The high excess CO2 values (>10 ppm) were associated with <20 m s−1 westerly and <10 m s−1 easterly. The Greater Tokyo Area is ~100 km wide, the distance a westerly air mass at <20 m s−1 would pass over in > ~1.5 hour. Along with the DME analysis, this result suggests that an adequate residence time of >1 hour over the metropolitan area provides measurable accumulation of CO2 up to ~1 km altitude in the overlying air mass. At the higher altitudes (Fig. 2a), transport of high CO2 was observed in the westerly at relatively high wind speed (>10 m s−1). It is again seen that the variability of excess CO2 is larger in the lower layer (Fig. 2c).

### Cities worldwide

We applied the above analysis to all of the 36 airports worldwide. At ~1 km altitude over many airports, we identified characteristic wind direction sectors where high CO2 events were observed, and in each case the wind direction corresponded well to the geographical location of the urban agglomeration of the nearby large city (Supplementary Fig. S3S36). High CO2 enhancements were usually observed at relatively low wind speeds (roughly < 15 m s−1). Vertical distributions of excess CO2 indicate that, in most cases, the ~4 km altitude is above the boundary layer, and thus the associated CO2 histograms reflect the free tropospheric conditions. In contrast, the histograms in the 1.0–1.5 km layer show considerable broadening at many airports, indicating the presence of nearby surface fluxes that cause fluctuations in CO2 in the overlying atmosphere. Therefore, at most airports, the lowermost altitude layers of the CONTRAIL measurements are under substantial influence of CO2 emissions from the nearby urban area.

The above results point to the possibility of a relationship between the magnitudes of atmospheric CO2 variability and of associated urban CO2 emission. We used standard deviation (SD) of excess CO2 as an indicator of the magnitude of the short-term CO2 variability observed at all airports (Fig. S2). We observed SD exceeding 5 ppm at heights 1 km and lower over several airports, but at every airport, it decreases to <2 ppm at higher altitudes, i.e. the free troposphere (Fig. S37). Although the SD varies seasonally at heights less than or around 1.0 km over some airports (e.g. NRT), the seasonality in the SD is not common over most airports. For the data analysis below, we therefore calculated the annual SD values, regardless of the data gaps at individual airports.

We found that CO2 variability at 1.0–1.5 km altitudes is largest over some Asian cities, and moderately large over some cities in Europe and North America (Fig. 3a–c). Large CO2 variability is associated with urban areas with largest populations in the world; for instance, Tokyo (corresponding airports are NRT and HND) is ranked as the world largest urban agglomeration by population in 2010, and Delhi (DEL), Mexico City (MEX), Shanghai (SHA), and Osaka (ITM and KIX), over which we found the large SD values, are all listed in the top 10 population cities11. The most airports with small SD and vertical gradient are located in coastal areas, and the associated cities are relatively small in CO2 emissions (Table S1).

We plotted the airport SD as a function of CO2 emission from the nearby associated city for 2010 (Fig. 3d). Here we aggregated CO2 emissions within 50 km to the east, west, north and south from a representative city center such as city hall, main station and local government building based on the ODIAC (Open-source Data Inventory for Anthropogenic Carbon dioxide, version ODIAC2015) dataset26,27. It is seen that, in the free troposphere (4.0–4.5 km), the SD is small (<2 ppm) over all the airports, irrespective of the intensity of CO2 emission from a nearby city (R2 = 0.16); in contrast, at the low altitude (1.0–1.5 km), the SD has a significant correlation with city CO2 emission (R2 = 0.73), suggesting considerable influence of the urban CO2 emissions on our measurements. A significant correlation (R2 = 0.68) is likewise observed for the data below 1 km, but with a larger scatter and a less compact correlation plausibly due to higher variability and less number of data. It is notable that there are some exceptional cities whose variabilities show excursions from the general trend; the SD values over Singapore (SIN), Los Angeles (LAX), and Chicago (ORD) are as small as those in the free troposphere; those over Hong Kong (HKG), Osaka (KIX), and Mexico City (MEX) are disproportionally high with large uncertainty. Here we used the ODIAC dataset, as it provides up-to-date gridded estimates of anthropogenic CO2 emissions. It is noted that the use of different anthropogenic CO2 emission datasets would not significantly affect the present result, given the fact that the existing CO2 emission datasets (including ODIAC), with their major differences originating in the downscaling of national totals, correlate well with each other at the spatial scale of the current study (100 km × 100 km) or even smaller28.

Despite various factors that could contribute to the CO2 variability over airports, our results strongly suggest that the intensity of the nearby urban CO2 emissions is the primary component of the magnitude of the observed CO2 variability (Fig. 3d). Our analyses of the wind pattern (Figs. 1, 2 and Supplementary Figs. S3S36) indicate that the CO2 variability at ~1 km altitude is, to a large degree, driven by the advection of high-CO2 air masses influenced substantially by CO2 emissions from the nearby city. It is likely that larger CO2 emissions enhance contrast of atmospheric CO2 mole fraction between their downwind and other locations, which makes fluctuations observed during multiple flights larger. The observed correlation may suggest that our lowest measurable altitude (1.0–1.5 km) is plausibly the height region where city-scale (~tens of km) emission imprint is distinct, and in which smaller-scale heterogeneity due to spatial pattern of emissions and local meteorology is relatively smoothed out. Previously, ground measurements in Paris showed that more urbanized part of the city showed larger CO2 variations due to spatiotemporal variations of nearby anthropogenic emissions15. Moreover, the present result is consistent with a previous modeling study23, which showed, by analyzing the CONTRAIL CO2 vertical profiles over NRT, that the magnitude of the atmospheric CO2 variability in the boundary layer is highly sensitive to the magnitude of anthropogenic local fluxes.

## Discussion

If we assume constant height of the convective boundary layer, one would expect a linear relationship between the surface CO2 emission and the enhancement of the CO2 mole fraction in the downwind boundary layer. In reality however, such emission-mole fraction relationship is complicated by the boundary-layer dynamics which undergoes significant daily and seasonal variations, causing fluctuations in the emission-driven CO2 accumulation in the boundary layer. Our vertical CO2 measurements were made under such varying meteorological conditions, likely a contributing factor in the variability in the SD values around the red line in Fig. 3d. In general, every airport has at least two opposite approach/departure directions along the runway, depending on the wind direction; flight routes are determined by airspace over the airport as well as by meteorological condition, thereby differ from flight to flight. We note that our observations might have been biased by specific flight routes under prevailing wind direction. The CO2 mole fraction would be elevated in downwind of a neighboring city when the aircraft enters “urban CO2 dome/plume” (Fig. 4a.c). In contrast, when the aircraft is positioned at upwind of the city, CO2 emissions from the city would be hardly captured, except in cases where the aircraft flies down over the city (Fig. 4b,d). The varying spatial extent of the CO2 dome/plume is another crucial factor in detecting urban emission signals. It is influenced by wind direction and speed, as well as the development and decay of convective boundary layer at the time of observation15,24. In this respect, the local time of the measurements is relevant, as commercial aircraft are scheduled at specific time of a day. Likewise, upwind biospheric CO2 fluxes that undergo significant diurnal and short-term (shorter than seasonal) variations could contribute to the observed variability. Relative contributions of these various factors would be dependent on the measurement location, which might contribute to the variability around the linear trend in Fig. 3d. Case studies dedicated to data analysis of these contributing factors are required to identify the nature and extent of influence of the local surface fluxes to the observed variations; our earlier work provides an example for Delhi (DEL), India24.

The variability-emission relationship in CO2 (Fig. 3d) could not have been found without the commercial airliner in-flight measurements that enable worldwide vertical CO2 scanning over large cities. We note that the relationship represents atmospheric CO2 variability obtained from the last 10 years of aircraft data plotted against the 2010 CO2 emission data. Given the above consideration (Fig. 4), it is reasonable to assume that this relationship would hold for other years of city emission data, and further analyses based on yearly or monthly time scale are required to establish this relationship on a much firmer ground. Currently the vertical profile data over Tokyo (NRT and HND), where the measurement is most frequent, might satisfy such requirement. The value of the results (Fig. 3), as interpreted within our conceptual frame (Fig. 4), becomes more obvious in contributing towards constraining anthropogenic CO2 emissions for cities in developing countries where uncertainty of emission inventory is large and atmospheric measurements available for top-down emission estimation are sparse.

We also explored the possibility of a relationship of vertical gradient (i.e., CO2 difference between ~1 km and the free troposphere) against city CO2 emissions, with a hypothesis that strong ground emissions would elevate the near-surface CO2 levels while the free troposphere is generally free from surface influence. In other words, vertical CO2 gradient could represent the aforementioned linear relationship with associated surface emissions. We found large vertical gradients at some airports with strong nearby CO2 emissions, however, we did not find a significant relationship between the vertical gradient and the city CO2 emissions for various cities. The calculated vertical gradient was found to be considerably dependent on measurement time, season and location of individual airports. As discussed above, CO2 variability over cities is influenced by various factors and, among them, the vertical extent of the CO2 dome/plume is of particular importance. It depends on the height of the convective boundary layer that varies seasonally and diurnally and influences the meteorological condition during vertical flight measurements. Seasonal coverage of the data and flight schedule are thus also relevant. Furthermore, geographical location of an airport relative to the nearby city varies significantly from city to city; thus, spatial representativeness of the observed vertical gradient differs among airports. Accordingly, for a global characterization of urban CO2 emissions based on vertical aircraft measurements at world’s major airports, as in this study, the vertical gradient would not provide a consistent relationship with corresponding city CO2 emissions due to uneven measurement opportunities at various airports. We however consider that it could be a good indicator of CO2 enhancement due to surface emissions for in-depth analyses at individual airports.

In summary, this study has demonstrated that the data taken by commercial airliners in airport proximity contain clear advective fingerprints of urban CO2 emissions. Better understanding of transport processes of local surface fluxes to the atmosphere for individual measurement locations is also needed. Although the observed variability of CO2 in the lower troposphere can be caused by many physical processes, the present study showed that the magnitude of the CO2 variability at an airport reflects the amount of CO2 emitted into the atmosphere from the corresponding city. The variability-emission relationship deduced from a relatively large number of vertical profile measurements could be helpful for evaluating surface fluxes and vertical propagation processes in the boundary layer simulated by various local to regional scale transport models. Further studies incorporating commercial aircraft data into urban CO2 emission studies will contribute significantly towards better estimates of CO2 emissions from major cities worldwide. Although vertical profile simulations by a regional transport model have been previously examined with commercial airliner carbon monoxide data29, the high-resolution vertical profile CO2 data used in this study should be considered for incorporation in urban-scale inversion studies30,31 or to be used in an independent validation of the emission estimations derived from ground-based data.

Although some recent projects have focused on urban CO2 monitoring and quantification of CO2 fluxes from cities, such as Paris15, Los Angeles14, Indianapolis13 and Toronto16, we still have long ways to go, particularly when it comes to addressing key upcoming megacities that include those in developing countries11,12. In this respect, the advantage of commercial airliner is that measurements could provide a great opportunity to study many cities that have not been probed by the current ongoing urban monitoring projects and contribute to the reduction in uncertainties in the estimates of urban CO2 emissions. The present study with Japan Airlines covers many cities in Asia where CO2 measurements are sparse and a new set up of secured long-term ground-site measurements is difficult. Although installation of a greenhouse gas measurement system into a European airline is in progress21, further implementation, in particular into airlines of the United States, China and United Kingdom whose commercial aviation operations together accounts for about 40% of the world32, will significantly extend global monitoring capability of urban areas. Measurements onboard several airlines at same airport will provide vertical profile data at different local-time schedules, which will be also helpful for better quantification of surface fluxes.

## Methods

### Experimental

The CONTRAIL project deploys Continuous CO2 Measuring Equipment (CME) and its in-flight measurements started on 5 November 2005. We refer to our earlier papers for details20,22,25,33. Briefly, the CME unit measures CO2 mole fractions onboard the aircraft using a non-dispersive infrared gas analyzer (LI-840, LI-COR Biogeosciences). As of October 2019, installation of the CME is certified for eight Boeing 777-200ER and two Boeing 777-300ER aircraft of Japan Airlines (JAL). Once installed, the CME is operated automatically using the aircraft’s flight navigation data from the ARINC 429 data bus until it is unloaded from the aircraft about two months later. The measured sample values are compared with two working standard gases (CO2 in air) installed inside the CME that are traceable to the NIES (National Institute for Environmental Studies)-09 CO2 scale. The NIES-09 CO2 scale defines mole fraction of CO2 in dry synthetic air in μmol mol−1 (reported in ppm in this paper). The results from the Round Robin intercomparison experiment show that the NIES-09 CO2 scale differs from the WMO-CO2-X2007 scale (http://www.esrl. noaa.gov/gmd/ccgg/wmorr/wmorr_results.php) by <0.1 ppm. The CME data are recorded at 10-s intervals during ascent/descent (~100-m intervals in altitude) and at 1-min intervals during cruise (~15-km intervals horizontally) as well as in-flight aircraft position, static air temperature and wind data received from the ARINC 429 system. To avoid heavy pollution around airports, CME is not operated within 2000 ft (609.6 m) of the ground surface (this altitude was set to 1200 ft in early years). The analytical precision of the CME is estimated to be <0.2 ppm.

### Data analysis

Here we examined atmospheric CO2 variations due to emissions from cities and local surface fluxes. It was assumed that the observed CO2 variation is composed of variations on different timescales e.g. interannual, seasonal and shorter-term variations, where local scale signals of our interest most likely contribute to the last term. It is noted that this term also contains synoptic-scale variations which represent signals of larger scale fluxes in space (i.e. regional). We therefore needed to subtract longer-timescale variations according to our earlier analysis25 as follows:

$$\Delta C{O}_{2}(lat,\,lon,\,alt,\,t)=C{O}_{2}(lat,\,lon,\,alt,\,t)\mbox{--}Trend\,C{O}_{2}\,at\,MLO\,(t)$$
(1)

Here lat, lon, alt, t are the latitude, longitude, altitude and time of individual CME data points, respectively, and Trend CO2 at MLO is the long-term trend curve calculated from the flask-based CO2 data at Mauna Loa (MLO; 19.54°N, 155.58° W, 3397 m.a.s.l.), Hawaii, obtained from NOAA/ESRL/GMD (National Oceanic and Atmospheric Administration/Earth System Research Laboratory/Global Monitoring Division; available at ftp://aftp.cmdl.noaa.gov/data/) with a digital filtering technique34. In general, the long-term CO2 trend at MLO is representative of the large-scale clean atmosphere and has been used as a reference site; thus, ΔCO2 in Eq. (1) gives an estimate of the climatological seasonal variations25,35 (see Supplementary Fig. S1). Next we calculated excess CO2 as follows:

$$excess\,C{O}_{2}(lat,\,lon,\,alt,\,t)=\,\varDelta C{O}_{2}(lat,\,lon,\,alt,\,t)-median\,\varDelta C{O}_{2}(airport,\,alt\mbox{--}bin,\,t\mbox{--}bin)$$
(2)

Here airport refers to the nearby airport where the vertical profile data are taken, alt-bin and t-bin are the altitude and time-of-the-year bins to which individual data points belong. Individual data points are grouped into 500-m altitude and 14-day bins (giving a total of 26 time bins per year). Note that altitude in this study refers to level above ground of the nearby airport (above ground level, a.g.l.). By subtracting the seasonally varying median values according to Eq. (2), excess CO2 represents detrended and deseasonalized variations and is analyzed below in terms of altitude and geographical locations. We also calculated SD of excess CO2 in each time bin and found that its seasonality is not common to the data over most airports (Supplementary Fig. S2). For statistical analysis, we selected 36 airports that contained sufficient number of vertical profiles over the 2005–2016 period; the number of vertical profiles ranged from 50 to >7000 (Supplementary Table S1).