Madrid is located on the Meseta Central and 60 km south of the Guadarrama mountains with a considerable altitude difference across the city, ranging from 570 to 700 m a.s.l.

This work was made in the framework of the MEGEI-MAD project (García et al., 2019), which aimed to measure atmospheric concentrations of GHGs in an urban environment combining FTIR instruments and ground-level analyzers. Another objective of MEGEI-MAD was to analyze the possible use of portable COCCON instruments to shape an operational network for Madrid in the future. The MEGEI-MAD project was initiated by the Izaña Atmospheric Research Center (AEMet), in cooperation with two German research groups (the Karlsruhe Institute of Technology and the University of Heidelberg) and two Spanish research groups (the Autonomous University of Barcelona and the University of Valladolid).

Within MEGEI-MAD, a 2-week field campaign was carried out from 24 September to 7 October 2018 in Madrid, where five COCCON instruments were located at five different places circling the metropolitan area (see Fig. 1). Table 1 summarizes the coordinates, altitudes of the COCCON locations and auxiliary meteorological data collected for data analysis of the observations. The locations have been chosen by considering the prevailing winds and the emission sources of CO2 and CH4, as well as other technical and logistic criteria (García et al., 2019, 2021).

The daily plume is modeled as a function of wind direction and wind speed. The schematic dispersion model for describing emissions assumes an expanding cone-shaped plume with the tip at the plume source at location 0,0. The plume cone has an opening angle of size α, and any grid cell within the cone is affected by the emission (see Fig. 2). The angle α is a technical parameter to schematically describe a spreading of the plume and is empirically adjusted to a value of 60∘. Different opening angles are modeled and presented in Fig. A1. The modeled plume has the most similar shape compared to the TROPOMI measured NO2 plume (see Sect. 3.3) when α>=60∘. If the grid cell x,y locates inside the cone, the column enhancement for this cell can be calculated by 3Δcolunm(x,y)=εv⋅d(x,y)⋅α, where ε is the emission strength at the source point in molec. s-1, v is the wind speed in m s-1, d is the distance between the downwind point and the source, and α is the opening angle of the plume in rad (here assumed to be 60∘).

The distance from a general grid cell x,y from the source is 4dx,y=x2+y2.

The enhanced dry-air volume mixing ratio for target species (ΔXVMR) at the center of the grid cell x,y can then be calculated by dividing the column enhancement by the total column of dry air (columndryair): 5ΔXVMR=Δcolunm(x,y)columndryair.

The columndryair is computed from the surface pressure: 6columndryair=Psmdryair⋅g(φ)-mH2Omdryair⋅columnH2O, where Ps is the surface pressure, mdryair and mH2O are the molecular masses of dry air (∼28.96 g mol-1) and water vapor (∼18 g mol-1), respectively, columndryair and columnH2O are the total column amount of dry air and water vapor, and g(φ) is the latitude-dependent surface acceleration due to gravity.

In this study, each individual landfill is considered an individual point source. The daily plumes from the individual landfills are super-positioned to have a total daily plume. The averaged enhancement of XVMR (plume) over the study area is computed for the selected wind sector. The plume for the opposite wind regime is also constructed in the same manner. The differences between these two data sets are therefore the wind-assigned anomalies (see Sect. 3.3). By fitting the modeled wind-assigned anomalies to the anomalies as observed by the satellite, we can estimate the actual emission strength (see Sect. B2). Note that the applied calculation scheme would also be extendible to areal sources by superimposing such calculations using different locations of the origin.

To detect whether TROPOMI is capable of measuring XCH4 precisely in the Madrid area, we perform intercomparison between TROPOMI and COCCON XCH4 measurements. Figure 3 shows the correlation between COCCON and TROPOMI measurements. The mean value of TROPOMI XCH4 is calculated by collecting observations within a radius of 5 km around each COCCON station. The coincident COCCON mean XCH4 is calculated from the measurements within 30 min before or after the TROPOMI overpass. The distance between two stations ranges between 6 and 14.2 km. The TROPOMI data within a circle with a larger radius might cover the information from other nearby stations, which brings an error in the correlation between the coincident data. Therefore, we choose a collection circle with a radius of 5 km for TROPOMI. The coincident data at each station show generally good agreement. Note that there are 1 to 2 TROPOMI measurements located within a circle of 5 km radius around each station. The mean bias in XCH4 between TROPOMI and COCCON is 2.7 ± 13.2 ppb, which is below the absolute bias between TROPOMI and TCCON (3.4 ± 5.6 ppb, Lorente et al., 2021a). The higher scatter of the validation with COCCON reflects the shorter temporal and spatial collocation, but the agreement indicates that TROPOMI data have good quality and a low bias.

The coincident data on 25 September 2018 and 4 October 2018 show large biases at Jose Echegaray station where the SN69 COCCON instrument is located. Due to its coarser spatial resolution, the TROPOMI XCH4 observations do not capture the local enhancements detected by the COCCON instrument in the vicinity of the source. Figure 4 illustrates the 2 example days of the time series of COCCON SN69 and coincident TROPOMI observations. Obvious enhancements are observed at around 13:00 UTC by the COCCON instrument in the downwind site on 25 September and at around 12:30 on 4 October 2018 (see Fig. A2 for the other days). Note that the XCH4 enhancements can also be observed by the instruments at other stations when the CH4 plume passes over Madrid. We only discuss the 2 representative days with obvious enhancements here, as we focus on the specific source near the Jose Echegaray station. The Valdemingómez and Pinto waste plants are located nearby, with a distance of 4.5 and 12 km, respectively. These five COCCON stations can serve as an independent source of information for constraining the wind speed. For example, the distance between the Jose Echegaray and Barajas is about 10 km. The highest anomalies of XCH4 arrived around 1.5 h later at Barajas station than they appeared at the Jose Echegaray station on 25 September 2018, which indicates an averaged wind speed of 1.8 m s-1. This value fits well with the wind velocity observed at the Cuatro Vientos Airport.

TROPOMI detected 10 ppb higher XCH4 at Jose Echegaray station than at Barajas station on 25 September 2018. However, COCCON observed a much higher amount of XCH4 (53 ppb) at Jose Echegaray station than at Barajas station (and other stations) at around 13:00 UTC. The delayed enhancements at AEMet and Barajas stations at the downwind direction are found after the wind direction changed from north more towards south direction. Another obvious enhancement of XCH4 is observed at Jose Echegaray station by the COCCON SN69 instrument at around 12:30 on 4 October 2018, with about 97 ppb higher XCH4 than COCCON measurements at the other four stations. However, TROPOMI only measured about 13 ppb higher XCH4 at Jose Echegaray station compared to the TROPOMI measurements at the other stations. These considerable enhancements at Jose Echegaray station observed by the COCCON instrument are likely due to the local source (the nearby Valdemingómez waste plant). The plume is in close vicinity to the source narrower than the pixel scale of the satellite, and therefore it is only detected as an attenuated signal by TROPOMI. The full width at the half maximum (FWHM) of the enhancement peak on 4 October 2018 roughly covers a temporal window of 30 min, with a corresponding wind direction change of 22.5∘ (∼ 0.4 rad) and an averaged wind speed of 1.0 m s-1. The distance between the COCCON SN69 to the Valdemingómez waste plant is about 4500 m. The 97 ppb enhancement measured by COCCON SN69 instrument yields an estimated emission strength of 3.7 × 1025 molec. s-1.

According to the Spanish Register of Emissions and Pollutant Sources (PRTR, http://www.en.prtr-es.es/, last access: 20 February 2021), more than 95 % of total CH4 emissions are from three waste treatment and disposal plants in the Madrid region (locations showed in Fig. 1). The annual CH4 emission rates from the PRTR for each plant are listed in Table 2. The total emission strength for each plant is about 2.5 × 1025 molec. s-1. This value only considers the “cells” in production, i.e., those where the waste is not yet covered with soil. The emissions from sealed cells are not included in the total emissions, but they still emit CH4 for years after sealing. So, the estimated emission rates from the inventories are expected to underestimate the true emissions, which fits reasonably with the estimated emission rate derived from COCCON measurements. The COCCON instruments show a very good ability to detect the source. Based on this evidence we investigate the potential of the TROPOMI and IASI CH4 products for detecting CH4 sources in the following.

To better represent the whole area of Madrid, the hourly ERA5 model wind at a height of 10 m around Madrid is used. ERA5 is the fifth-generation climate reanalysis produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) (Copernicus Climate Change Service, 2017). The TROPOMI overpasses over Madrid cover the time range from 12:00–14:30 UTC (IASI overpasses are typically from 09:30–10:30 UTC), but the dispersion of emitted CH4 is influenced by the ground conditions (e.g., wind speed and wind direction) over a wider time range (Delkash et al., 2016; Rachor et al., 2013). Therefore, the wind information between daytime (08:00–18:00 UTC) is chosen to define the predominant wind direction for each day. Figure 5 presents the wind roses for daytime between 10 November 2017 and 10 October 2020 (the first and last day with valid TROPOMI data). The dominating wind direction was southwesterly. The Guadarrama mountains and the Jarama and Manzanares river basins are located the northwest of Madrid, and they influence the air flow. Therefore, we use a wider wind range for the specific wind area in this study to cover the dominant wind directions, i.e., SW for the range of 135–315∘ and NE for the remaining direction. If a wind direction dominates 60 % of records for 1 d, i.e., if the wind direction belongs to one specific area more than 60 % of the daytime (08:00–19:00 UTC), then this predominant wind direction is selected for that day. The SW and NE wind fields are used for constructing wind-assigned anomalies in this study, and we demonstrate this construction by using TROPOMI nitrogen dioxide (NO2) data in the next section. Table 3 summarizes the number of days and wind speed for each specific wind area. The wind direction during the TROPOMI overpasses was 61.8 % in the SW wind field and 28.4 % in the NE wind field, and their averaged wind speed is similar.

When fossil fuels are burned, nitrogen monoxide (NO) is formed and emitted into the atmosphere. NO reacts with O2 to form NO2 and with ozone (O3) to produce O2 and NO2. NO2 is an extremely reactive gas with a short lifetime of a couple of hours and has lower background levels than CH4 (Kenagy et al., 2018; Shah et al., 2020). It is measured by TROPOMI with excellent quality. Therefore, it is a suitable proxy for demonstrating the method developed for the wind-assigned anomaly.

TROPOMI offers simultaneous observations of NO2 columns. The recommended quality filter value for the analysis of TROPOMI NO2 columns is qa_value > 0.75 (http://www.tropomi.eu/sites/default/files/files/publicSentinel-5P-Level-2-Product-User-Manual-Nitrogen-Dioxide.pdf, last access: 11 November 2021). Based on the predominant wind direction in Madrid (see Sect. 3.2), the averaged wind-assigned anomalies are defined here as the difference of the mean TROPOMI NO2 column under the wind direction from NE and the mean TROPOMI NO2 column under the predominant wind direction of SW in Madrid.

Figure 6a illustrates the wind-assigned anomalies of TROPOMI NO2 (ΔNO2) on a 0.1∘ × 0.135∘ latitude–longitude grid during 2018–2019. Pronounced fusiform-shaped plumes are observed along NE–SW wind direction as expected. Figure 6b shows the wind-assigned anomalies derived from the simple model introduced in Sect. 2.3, using Madrid city center as the point source with an assumed emission rate (ε) of 5.0 × 1024 molec. s-1 and using ERA5 10 m wind data. The similar symmetrical positive and negative plumes to those in Fig. 6a imply that our method of wind-assigned anomaly is working as anticipated, that the ERA5 10 m data are indeed representative for the area and that the implementation of the satellite data analysis is correct. Figure 6c shows the strong correlation between the wind-assigned anomalies derived from the TROPOMI measurements and the simple plume model (ε=5.0 × 1024 molec. s-1). Using the fitting method as described in Sect. B2, we estimate an emission rate of 3.5 × 1024 molec. s-1 ± 3.9 × 1022 molec. s-1. Here the uncertainty is due to the noise of the observations and is calculated according to Eq. (B15) (Appendix B). This estimated source strength is weaker than the strength obtained by Beirle et al. (2011), where the reported NOx emission is around 150 mol s-1 in Madrid, corresponding to a NO2 emission of 6.8 × 1025 molec. s-1. It is because our model does not consider the decay of NO2, which results in a lower emission rate.

The result of this test using NO2 also allows the angular spread parameter used in the plume model to be adjusted (see Sect. 2.3 and Eq. 3). As it can be seen from Fig. A1, assuming an angular spread of 60∘ reasonably reproduces the shape of the plume.

CH4 has a relatively longer lifetime as compared to NO2, and its background in the atmosphere is high. An increasing trend with obvious seasonality and strong day-to-day signals for XCH4 is seen in Fig. 7 (upper panels). Therefore, these background signals need to be removed before simulating the wind-assigned anomalies (see Sect. B1). After removing the background, the anomalies (raw data – background) represent more or less the emission from local area (Fig. 7 lower panels).

Figure 8 illustrates the anomalies of XCH4, TXCH4 and UTSXCH4 for all measurement days, days with predominating SW wind field and days with predominating NE wind field. The distributions over the whole area for XCH4 and TXCH4 are similar, and no obvious enhancement is observed in UTSXCH4, as expected, since CH4 abundances dominate in the troposphere. The areas where the three waste plants are located show obvious high anomalies in the figures (Fig. 8a and d) when the data are averaged over all days for all wind directions and in the downwind direction (Fig. 8b, c, e and f), demonstrating that our method of removing the background works well and the satellite products can detect the local pollution sources after removing the background. Enhanced plumes of XCH4 and TXCH4 are better visible on the downwind side of SW than on the downwind side of NE wind field. This is because the SW is the most dominant wind direction, and the SW plume signal is based on a higher number of data and thus less noise.

The wind-assigned anomalies derived from XCH4 anomalies and TXCH4 anomalies on a 0.1∘ × 0.135∘ latitude–longitude grid are presented in Fig. 9. The XCH4 and TXCH4 wind-assigned anomalies show similar bipolar plumes but are more disturbed compared to those derived from NO2. This is because the CH4 signal is weak compared to the background concentration, so the noise level of the measurement and the imperfect elimination of the background are significant disturbing factors.

Based on the knowledge of the locations of the three waste plants, we choose their locations as point sources to model the enhanced XCH4 according to the wind information. The initial emission strength is 1 × 1026 molec. s-1 in total, and the emission rate at each point source is repartitioned among these three sites according to Table 2. The modeled and observed wind-assigned anomalies show a reasonable linear correlation (coefficient of determination R2 of about 49 % and 44 % for XCH4 and TXCH4, respectively) with observed ΔXCH4. Based on Eq. (B12) (Appendix B), we obtained an estimated emission rate of 7.4 × 1025 ± 6.4 × 1024 molec. s-1 for XCH4 and 7.1 × 1025 ± 1.0 × 1025 molec. s-1 for TXCH4. The uncertainty values given here are the square root sum of the uncertainty due to the background signal and the data noise, which are calculated according to Eqs. (B14) and (B15) (Appendix B). Figure 9g, h and i show the wind-assigned anomalies for UTSXCH4. For the modeled UTSXCH4 anomalies we assume here the CH4 enhancement to occur at altitudes between 7 and 20 km a.s.l. As expected, the fit of these model data to the observed UTSXCH4 data yields emission rates close to zero (1.4 × 1025 ± 7.2 × 1024 molec. s-1), revealing that there is no significant plume signal above 7 km a.s.l. The fact that for TXCH4 we obtain practically the same emission rates as for XCH4 and that in the UTSXCH4 data we see almost no plume nicely proves the quality of our careful background treatment method and the low level of cross sensitivity between the TXCH4 and UTSXCH4 data products. The applied background treatment allows detecting the near-surface emission signal consistently in the total column XCH4 data and in the tropospheric TXCH4 data.

Figure 10 illustrates the estimated emission strengths for the different products. The emission strengths derived from the satellites are higher than the ones derived from COCCON measurements, as TROPOMI covers a larger area, while COCCON measurements are only sensitive to local sources from the nearby waste plant. The PRTR inventory document gives lower values than our results. This is probably because it only lists the active landfill cells and does not include the closed ones in Madrid, which probably still emit for many years (Sánchez et al., 2019).

The point sources and their proportion in the total emission rate in this study are based on the a priori knowledge of three different waste plant locations. If we use a single source located at the Pinto waste disposal site only, it yields an emission rate of 6.3 × 1025 molec. s-1, ∼ 15 % lower than that of the three point sources for CH4 and 6.0 × 1025 molec. s-1 (-15 %) for tropospheric CH4 (see Fig. 10). The opening angle (α) is experimentally selected based on the comparison between the TROPOMI measured and modeled NO2 plume, which results in some uncertainties as well. Using 90∘ instead of 60∘ for α in the plume model results in an emission strength of 7.6 × 1025 molec. s-1 (+3 % change) for CH4 and of 7.4 × 1025 molec. s-1 (+4 % change) for tropospheric CH4.

The surface wind can be influenced by the topography, and the actual transport pathway from the emission source to the measurement station is difficult to know (Chen et al., 2016; Babenhauserheide et al., 2020). To study the wind sensitivity, the hourly wind information measured at the Cuatro Vientos Airport at 10 m height is used instead of the ERA5 10 m wind. There are other in situ measurements available but not used here, as the AEMet headquarter station is affected by nearby buildings and the Barajas Airport station is very close to a river (Jarama) that determines a specific wind pattern. The wind measured at the Cuatro Vientos Airport is quite different compared to the ERA5 wind, as in situ-measured NE wind becomes dominant as well, and the wind speed in SW wind field increases by ∼ 50 % compared to that of ERA5 wind (Figs. A3, A4 and Table A1). Using the wind measured at the Cuatro Vientos Airport results in an emission rate of 7.7 × 1025 molec. s-1 (+4 %) for CH4 and 9.5 × 1025 molec. s-1 (+34 %) for tropospheric CH4.

In summary, the uncertainties derived from the source location, opening angle or wind cannot be ignored, but nevertheless the emission rates estimated from the spaceborne observations are clearly larger than the values reported in Table 2 and are larger than the ones estimated from the COCCON SN69 observations in October 2018.