CO2, carbon monoxide (CO) and nitrogen oxides (NOx=NO+NO2) fields were simulated with the COSMO-GHG model, which is a version of the non-hydrostatic regional weather prediction model COSMO extended for the simulation of passive trace gases such as greenhouse gases . The simulations were conducted for a domain centered over the city of Berlin and covering a large number of power plants in Germany and neighboring countries. The simulation spans the whole year 2015 with 1km×1km spatial resolution. Initial and boundary conditions were provided by the operational COSMO-7 analyses of MeteoSwiss for meteorology with 7 km horizontal resolution, by the Copernicus CAMS operational products for NO and NO2 with 60 km resolution , and by special high-resolution runs of ECMWF for CO and CO2 with 15 km resolution . Anthropogenic emissions were taken from the TNO/MACC-3 inventory (7km×7km resolution) (, for version 2) and were merged with a detailed inventory for Berlin provided by the city authorities . The emissions were vertically distributed according to predefined vertical profiles per source category. For large point sources, plume rise was computed explicitly to account for the varying meteorological conditions . Temporal variability was prescribed using fixed temporal profiles for hourly diurnal, weekly and seasonal variations per source category. Biospheric CO2 fluxes were computed offline by the Vegetation Photosynthesis and Respiration Model (VPRM) at 1km×1km spatial and hourly temporal resolution .

The simulations included a total number of 50 different tracers of CO2, CO and NOx that represented different sources and release altitudes and included background tracers constrained at the lateral boundaries by the global-scale models. Two CO2 tracers were included that represent biospheric CO2 fluxes due to respiration and photosynthesis. To account for NOx chemistry in a simplified way, the NOx tracers slowly decay with an e-folding lifetime of 4 h. NOx concentrations were converted to NO2 concentrations offline using an empirical formula that is often used for representing NOx-to-NO2 ratios downstream of emission sources .

Only a small number of these tracers were used in the present study. We used two CO2 and two NO2 tracers representing time-constant and time-varying emissions of Berlin, respectively. Furthermore, we created background tracers that contain CO2 or NO2 fields from all emissions and biospheric fluxes as well as inflow from lateral boundaries except for the emissions of Berlin.

The CO2M mission is a proposed constellation of polar-orbiting satellites with Equator crossing times around 11:30 local time . The main payload will be an imaging spectrometer for retrieving CO2 from measurements in the near-infrared and in two shortwave infrared spectral channels. The current system concept envisages a pixel size of 4 km2 and a swath width of at least 250 km. CO2M will also provide additional measurements of NO2, aerosols and clouds.

Synthetic satellite observations of column-averaged dry air mole fractions of CO2 (XCO2) and NO2 tropospheric columns were generated for a hypothetical constellation of six CO2M satellites with 2 km × 2 km spatial resolution and 250 km wide swaths. Each satellite has a sun-synchronous orbit with an overpass time of 11:30 local time and a repeat cycle of 11 d. The individual satellites are distinguished by their Equator starting longitude for the first orbit, which was chosen such that the satellites are spaced with equal angular distance in a common orbit. The constellation of six satellites has therefore angular distances of 60∘. The individual satellites are designated by the letters a to f.

With a constellation of six satellites Berlin could be observed every day. For more realistic scenarios with fewer satellites, the constellation was divided into constellations of one, two or three satellites (still with equal angular distances). This allows investigating the impact of the size of the constellation on the accuracy of the estimated CO2 emissions.

The error characteristics of the CO2 and NO2 measurements were specified in the SMARTCARB project in close collaboration with ESA . For XCO2, three uncertainty scenarios were prepared with 0.5, 0.7 and 1.0 ppm random noise for a ground pixel with a vegetation surface and a solar zenith angle of 50∘ (VEG50 scenario). The random errors were calculated based on solar zenith angle and surface reflectances using the error parametrization formula of . Amplifications of the random errors in the presence of cirrus clouds and aerosols as well as the influence of systematic errors on the XCO2 measurements were not considered in our study. For NO2 columns, we only used the high-noise scenario with a reference noise σref of 2×1015 cm-2 or 20 % – whatever was larger. The NO2 noise was further modified based on cloud fraction roughly doubling the noise at 30 % cloud fraction. Table  summarizes the uncertainty scenarios.

The synthetic observations were flagged as cloudy using the total cloud fractions simulated with the COSMO-GHG model. Since the CO2 retrieval requires strict cloud filtering, we removed all pixels with cloud fractions larger than 1 %. NO2 retrievals can tolerate higher cloud fractions. We used a cloud threshold of 30 % to flag cloudy pixels as often applied in satellite NO2 studies e.g.,.

The analytical inversion uses the CO2 tracer representing the anthropogenic emissions of Berlin as simulated by the COSMO-GHG model. The method thus assumes perfect knowledge of atmospheric transport, which allows isolating the uncertainties in the flux inversion due to instrument noise. The inversion uses a forward model that computes the vector ymod of size m of model-simulated values at the locations of all XCO2 measurements within the plume. The plume was defined as those pixels for which the enhancement of the tracer is larger than a typical variability of the background field set to 0.05 ppm. The vector ymod is given by the equation 1ymod=Hx+yBG, where x is a scalar representing the CO2 emission strength of Berlin. H is the observation operator representing the sensitivity of the XCO2 signal to changes in x, i.e., the emissions, in the satellite image. Since x is a scalar, H is a row matrix. It contains all XCO2 values obtained from the CO2 tracer simulated with constant emissions of Berlin that are larger than 0.05 ppm. yBG is the XCO2 background, which was computed from the model-simulated fields excluding the emissions from Berlin, consistent with the assumption of a perfect model with accurately known transport and anthropogenic and biospheric fluxes outside of Berlin.

The emission of Berlin was found as the maximum likelihood optimal estimate by minimizing the following cost function: 2χ2(x)=(yobs-Hx-yBG)TSε-1(yobs-Hx-yBG), where yobs is the measurement vector containing the synthetic XCO2 observations. Sε is the error covariance matrix of the model–observation mismatch, which in our case of a perfect transport model corresponds to the measurement error covariance matrix. The diagonal elements of the error covariance matrix were set to the square of the absolute noise specified in Table .

The analytical inversion was applied to synthetic satellite observations with constant and time-varying emissions of Berlin. The uncertainty of the estimated emission was taken from the covariance matrix estimated by the least square fit. As a second measure of uncertainty, we computed mean bias (MB) and standard deviation (SD) of the differences between estimated and true emissions. Thereby, the true emission was taken at 10:30 UTC during satellite overpass. The plume may also contain emissions emitted earlier in the day, but the observation operator does not include information about the temporal variability of emissions. The variation in the diurnal cycle of emissions is rather small in the hours prior to the satellite overpass (Fig. S1 in the Supplement). Relative errors were computed relative to the annual mean at overpass time, which is 16.9 MtCO2yr-1 for constant and 20.0 MtCO2yr-1 for time-varying emissions. The latter is higher because emissions at 10:30 UTC are larger than daily mean emissions.

The mass-balance approach estimates CO2 emissions from a city plume detected by a plume detection algorithm. The approach calculates CO2 mass fluxes from plume signals that are obtained by subtracting a background field from the satellite observations. The plume signal is then integrated perpendicular to the direction of propagation of the city plume to obtain line densities that are multiplied with an estimate of the wind speed to obtain the fluxes. Under the assumption of steady-state conditions, these fluxes are equivalent to the emissions.

The plume detection algorithm described in was applied to determine the position of the CO2 plume in the satellite observations. The algorithm was applied either to the XCO2 observations or to the auxiliary NO2 observations. As shown in , the NO2 plumes largely overlap with the XCO2 plumes despite the fact that NOx is released in the model primarily at the surface by traffic emissions, whereas a larger proportion of CO2 is released from stacks at higher altitudes. The number and size of the detected plumes was significantly larger when the algorithm was applied to the NO2 measurements due to their better signal-to-noise ratio and lower sensitivity to clouds.

To obtain the plume signal, the background needs to be subtracted from the satellite observations. The CO2 background was estimated from the pixels surrounding the plume assuming that it is spatially smooth. To compute the background, all pixels within the detected plume were masked and replaced by interpolated values obtained by normalized convolution applied to the unmasked pixels surrounding the plume. The normalized convolution was performed with a Gaussian filter with σ = 10 pixels, i.e., a width of the Gaussian kernel of about 20 km.

Figure a shows a sketch of an CO2 city plume. To compute line densities, we draw 10 km wide boxes (nearly rectangular polygons) perpendicular to the plume's centerline. Line densities were computed for each box. Figure b shows the CO2 signals (in kgm-2) for one of the boxes. Choosing a box rather than a single line across the plume reduces the impact of noise and data gaps due to the larger number of available pixels. The across-plume width of the polygons is given by the maximum width of the detected plume plus an additional boundary of at least 10 km on each side to ensure that the entire plume is within the polygon even if only a part of the plume was detected.

The centerline of the plume was computed by fitting a two-dimensional curve to pixels within an extended plume area, which consisted of the detected plume as well as pixels within 50 km distance of the plume or the source. The surrounding pixels help stabilize the fit at the beginning and at the end of the detected plume. For the curve fit, pixels were weighted with the local mean values above background calculated by the plume detection algorithm. Outside the detected plumes, pixels were weighted either with a small value of 0.05 ppm or 0.2×1015 molec.cm-2 depending on whether CO2 or NO2 was used for plume detection. The two-dimensional curve p(r) consists of two parabolic polynomials: 3px(r)=a0r2+a1r+a2,4py(r)=b0r2+b1r+b2, with coefficients ak and bk and radial distance r. The parameter r is calculated as the distance from the origin: 5r=(x-xo)2+(y-yo)2, where x and y are easting and northing in the DHDN/Soldner Berlin spatial reference system (EPSG: 3068). The origin (xo, yo) is placed at least 50 km away from the source in the direction opposite to the plume, i.e., in the west of Berlin if the plume is in the east and vice versa. Figure a shows the centerline with its origin O and the location of the source S.

To draw the polygons, pixel coordinates need to be converted to along- and across-plume coordinates for each satellite pixel. The across-plume coordinate yp is the distance between pixel P and the curve at radial distance rp, i.e., point Q in Fig. , for which the line from Q to P is perpendicular to the curve. The along-plume coordinate xp is the arc length of the center curve from the source origin S to Q. xp and yp were calculated with a computationally efficient analytical solution as presented in the Supplement.

To compute line densities from the CO2 columns inside the polygons (e.g., Fig. b), we tested two options: (1) integrating in across-plume direction yp by adding up the plume signals cp of all pixels whose center point is within the polygon and (2) fitting a Gaussian function to the plume signals in across-plume direction and computing its integral. The first method does not make any assumption about the shape of the cross section, which is an advantage for city plumes that can be quite complex. The disadvantage is that it is more difficult to deal with missing pixels, which lead to an underestimation of line densities if not properly accounted for. To solve this issue, we sub-divided the polygons in across-plume direction in 5 km wide sub-polygons, for which we computed a mean value from the available pixels. Finally, we integrated over the mean values of the sub-polygons. Polygons were not used if the mean values of at least one of the sub-polygons with detected plume pixels could not be computed due to missing values. Note that this criterion rejects more line densities from plumes detected from the NO2 observations than from the CO2 observations, because the latter detect narrower plumes.

The second method has been used, for example, by . Fitting a Gaussian curve has the advantage that it automatically interpolates missing values. The disadvantage is that the transects of a city plume do not necessarily resemble a Gaussian curve. The Gaussian curve can be written as 6cp(y)=q2πσexp⁡-(y-μ)22σ2, with line density q, shift μ and SD σ. To avoid misfits, especially when pixels near the center of the plume are missing, a Gaussian curve was only fitted if at least one valid observation was available in each sub-polygon in the transect. When NO2 observations are available, it is also possible to simultaneously fit a Gaussian curve to the NO2 observations using the same SD σ for both the CO2 and NO2 curve. Since the NO2 observations have a higher signal-to-noise ratio, the width of the CO2 curve is constrained by the NO2 observations. This method was demonstrated by and is used here as a third method.

An estimate of the mean flow speed within each plume transect is required to convert line densities to emissions. The mean flow speed is the projection of the CO2-weighted wind vector onto the along-plume direction. Because we assume not to know the vertical and horizontal distribution of winds and CO2 concentrations sufficiently well from a model, we take the average wind speed at the location of Berlin in the lowest 500 m above surface assuming a well-mixed boundary layer as a rough estimate. The wind profile was taken from the COSMO-GHG model simulations at satellite overpass time but could be taken from any meteorological analysis data. Not taking the wind speeds directly at the locations of the cross sections was an attempt to account for uncertainties in the simulated winds that would be encountered with real rather than synthetic observations. To estimate the uncertainty in this simplified estimate of the mean flow speed, we also computed an effective wind speed for each polygon, taking into account the three-dimensional distribution of winds and CO2 mass concentrations. The effective wind speed is the weighted mean wind speed parallel to the plume's centerline and weighted by the partial CO2 mass column density of the plume. These CO2 column densities are taken from the model tracer that contains only emissions of the city.

Figure c shows line densities computed in along-plume direction. The line densities are zero upstream of the source, build up over the city and remain constant downstream of the city. The fluxes were obtained by multiplying the line densities with the wind speed. Finally, the fluxes were averaged to obtain an estimate of the mean source strength. We only considered values more than 10 km downstream of the city center to ensure that fluxes are obtained from outside of the city area. Uncertainties in the mean source strength were computed from the standard error of the individual line densities as well as by comparing with the true emissions at overpass.

To better understand the individual error components, the differences between estimated and true emissions were further analyzed using the detailed information available from the simulation. For this purpose, the mass-balance approach was additionally applied to the detected plume using the noise-free XCO2 observations, the true CO2 background and the effective wind speed. By replacing the uncertain information obtained from the observations with the accurate information from the model, four different types of error were distinguished.

The method error is the difference between the true emissions at satellite overpass and the emissions computed using the model information. It represents the intrinsic uncertainties of the method that arise from simplified assumptions such as constant emissions and wind speed, from the plume detection algorithm, and from the fitting of the centerline.

To estimate annual emissions and their uncertainties, the temporal variability of emission has to be considered, which includes seasonal, diurnal and weekend vs. weekday variations. Without accounting for this variability, annual mean estimates derived from a small sample of satellite overpasses at a fixed time of the day may be significantly biased.

In this study, only the seasonal cycle was estimated using a Hermite spline with periodic boundary conditions (see Supplement). The periodic boundary conditions help constrain the cycle in winter months, where only few data points are available. To properly fit the seasonal cycle, we used a spline with four equidistant knots. The annual emissions were then estimated by integrating over the seasonal cycle. The uncertainty of the annual emissions was estimated by error propagation from the precision of the CO2 emission estimates at individual satellite overpasses. Since annual emissions estimated in this way are only representative of emissions a few hours before the satellite overpass, the estimated emissions were compared with the emissions at overpass time. Uncertainties in the ratio between emissions at overpass time and daily mean emissions are thus not taken into account.

The analytical inversion was applied to all CO2 plumes observed by the CO2 satellites for constant and time-varying emissions and for the low-, medium- and high-noise scenarios with σVEG50 of 0.5, 0.7 and 1.0 ppm, respectively. Figure a and c show the time series of estimated CO2 emissions for the medium-noise scenario (σVEG50=0.7ppm) with a constellation of three satellites. CO2 estimates with uncertainties larger than 10 Mtyr-1, i.e., 50 % of the mean emissions at satellite overpass time for time-varying emissions, were discarded to remove plumes with very weak CO2 signals or with a small number of pixels.

The boxplots (Fig. b and d) summarize the differences between estimated and true emissions for all plumes observed by the six satellites. A constellation of six satellites was able to estimate emissions successfully, i.e., with an uncertainty smaller than 10 Mtyr-1, for 60 to 74 overpasses for time-constant emissions and 59 to 73 overpasses for time-varying emissions depending on the noise scenario. The average number of successful estimates was 11 per satellite and year but with a large range from 5 to 17 because of varying cloud coverage and because some orbits cover Berlin less frequently than others. Table  shows mean bias (MB) and standard deviation (SD) of the differences between estimated and true emissions. To compute comparable statistics for each instrument scenario, the statistics were computed only for the 60 and 59 plumes, respectively, for which the uncertainties were less than 10 Mtyr-1 in all three noise scenarios.

The constant emissions are generally well captured within the uncertainty range determined by the measurement noise. The uncertainties of the individual estimates vary strongly because the amplitudes and sizes of the plumes differ from case to case due to differences in wind speeds, cloud cover and incomplete coverage of the plume by the swath. The MB is close to zero for all noise scenarios.

In the case of time-varying emissions, the seasonal cycle of the emissions can be reproduced quite accurately because many plumes can be observed with three or more satellites and because the individual estimates have an average uncertainty of only 14 %–21 % depending on instrument noise scenario. The rare opportunities for observing plumes in winter due to frequent cloud cover, however, can easily be missed by a small constellation of satellites, which will make it difficult to reliably trace the seasonal cycle. The MB slightly deviates from zero (Table ) mainly because the observation operator H was calculated assuming constant emissions, while the measurement vector contains observations of time-varying emissions from several hours before the satellite overpass time. The SDs of the differences between the individual emission estimates and the true emissions are 3.0, 3.4 and 4.2 Mtyr-1 for σVEG50 of 0.5, 0.7 and 1.0 ppm, respectively (Table ). These values agree well with the mean of the estimated uncertainties, suggesting that the error propagation yields a realistic estimate of uncertainties.

The theoretical uncertainty computed by the inversion agrees well with the SDs computed for constant and time-varying emissions in Table . This estimated uncertainty depends on the number of pixels and the signal strength of the plume. The signal strength in turn depends on the wind speed and turbulent mixing. Figure  shows the dependency of the theoretical uncertainty on the inverse of the square root of the number of pixels and on wind speed for the medium-noise scenario. Fitting a robust linear regression model yielded 7σem=(91.5±3.8)σVEG50n+(0.32±0.08)uMtyr-1, with number of pixels n and wind speed u. The uncertainty depends strongly on the number of pixels and is smaller than 10 Mtyr-1 (50 %) if the number of pixels is larger than 100 for all three noise scenarios. The dependency on wind speed is less robust and does not depend on the noise scenario. Most outliers are due to plumes of less than 100 pixels. Note that the fit coefficients are specific to the emissions and meteorological conditions of Berlin and cannot be generalized for other cities.

The mass-balance approach was applied to synthetic observations of the CO2M mission for a constellation of up to six satellites using the uncertainty scenarios with σVEG50 of 0.5, 0.7 and 1.0 ppm. The location of the CO2 plumes was either detected from the CO2 observations alone or from the additional NO2 observations on board the same satellite.

As expected, uncertainties in the estimated emissions are larger for the mass-balance approach compared to the analytical inversion. Figure b and d show the difference between estimated emissions and the emissions at overpass for different noise levels of the CO2 instrument. These boxplots include all estimates for a constellation of six satellites.

Table  shows MB and SD of these differences. For better comparability, these statistics were computed only from those plumes that could be detected with all three noise scenarios, i.e., 16 plumes in the case of CO2-based detection and 34 plumes in the case of NO2-based detection. SDs are about 10 Mtyr-1, i.e., about 50 % of the 20.0 Mtyr-1 emissions of Berlin at overpass time, which is about 3 times larger than for the analytical inversion. For the plume detection based on the CO2 observations, SDs are about 9 Mtyr-1 (45 %) and, interestingly, do not depend significantly on the noise level of the instrument. SDs are slightly larger with 10 Mtyr-1 (50 %) if the NO2 observations are used for plume detection, because applying the mass-balance approach to larger plumes is more challenging.

The MB is positive for both CO2- and NO2-based plume detection. With NO2-based plume detection it rises slightly from 2.6 to 3.5 Mtyr-1 (13 %–17 %) from the low to the high-noise scenario. With CO2-based detection, in contrast, the lowest MB is surprisingly obtained for the high-noise scenario.

The MB is caused by systematic errors in the method, retrieval, background and wind errors, which can have substantial systematic errors that may add up or compensate for each other in the total error. The results therefore need to be interpreted with great care. MB and SD of the individual error components are summarized for the different noise scenarios in Figs.  and for CO2 and NO2-based plume detection, respectively. The method and total errors are computed against the true emissions at overpass, while the other errors are compared to the emissions computed using the model information. The total errors are identical to the errors presented in Table . The relative MB and SD are tabulated in the supplement. The different errors are discussed in detail in the following.

The results up to now focused on estimated emissions at individual satellite overpasses. To obtain annual emissions (at overpass time), seasonal cycles were fitted to the individual estimates of the analytical inversion and the mass-balance approach. For the analytical inversion, the uncertainty of the individual estimates were taken from the uncertainties obtained from the algorithm. For the mass-balance approach, we used an uncertainty of 10 Mtyr-1 (50 % of emissions at overpass) based on the estimated uncertainties in the approach. The results are shown only for the medium-noise scenario and for the method where line densities were computed from the mean values in the sub-polygons.

Figure a and c show the seasonal cycle fitted for a constellation of three satellites to the emission estimated by the analytical inversion. For the time-constant emissions, the annual emissions obtained from the fitted seasonal cycle (17.5±0.4 Mtyr-1) agree well with the true annual emissions (16.8 Mtyr-1). For the time-varying emissions, the seasonal cycle is also fitted well, but emissions are slightly overestimated in winter where no emission estimates are available. As a result, the estimated annual emissions of 21.6±0.4 Mtyr-1 are slightly larger than the true emissions at overpass (20.0 Mtyr-1).

Since the number of estimates is lower with the mass-balance approach, fitting the seasonal cycle is more challenging, in particular, for the few estimates from the CO2 observations alone (Fig. a). Nonetheless, annual emissions were estimated quite well with 20.9±3.8 Mtyr-1 for a constellation of three satellites. If NO2 observations are used for detecting the plumes, the temporal coverage is better and the seasonal cycle is fitted better, but emissions are overestimated in early summer. As a result, annual emissions are also higher with 22.3±2.5 Mtyr-1.

To analyze the effect of constellation size, we estimated annual emissions for constellations of one, two, three and six satellites (Fig. ). Under the assumption of a perfect model, the analytical inversion is able to estimate annual emissions well for both constant and time-varying emissions even with only one satellite (panels a and b) with an average precision of 1.1 Mtyr-1 (5.5 %). The time-varying emissions are slightly overestimated, because the fitted seasonal cycle tends to overestimate emissions in winter due to missing satellite overpasses in these months.

In contrast, estimating annual emissions with the mass balance is very difficult if only the CO2 observations are available for detecting the location of the plume. For a single satellite, the number of overpasses with successful emission estimates is too small to fit a seasonal cycle in nearly all cases, and even with two or three satellites the precision is low with about 8.8 Mtyr-1 (44 %). The situation significantly improves with additional NO2 observations. A single satellite can estimate annual emissions in five out of six cases with an average precision of 5.1 Mtyr-1 (26 %) due to the better temporal coverage. The average precision increases to 4.4 Mtyr-1 (22 %) and 2.5 Mtyr-1 (13 %) for constellations of two and three satellites, respectively. The annual emissions are slightly overestimated, because of low temporal coverage in winter and because the mass-balance approach is also sensitive to emissions outside of Berlin.

To estimate annual emissions accurately, it is necessary to resolve the real temporal variability of emissions. It should be noted that the temporal variability in the COSMO-GHG simulations used for generating the synthetic satellite observations likely underestimates the real variability. To generate temporally varying emissions in the simulations, we applied different diurnal, weekly and seasonal cycles to emissions from different sectors such as energy production, traffic and heating . These fixed time profiles do not account for effects from meteorology and human drivers such as strikes, temporal traffic restrictions or holidays.

To resolve the temporal variability, a sufficiently large number of individual emission estimates is required. The number of estimates varies strongly between satellites due to the uneven distribution of cloud-free days. Even with the NO2 observations, it is still possible to have only four overpasses with estimated emissions per year with two satellites. Therefore, at least three satellites are likely necessary to get reliable estimates of the annual emissions. Higher temporal coverage can alternatively be achieved by increasing the swath width of the instrument.

Besides day-to-day variability of emissions, individual emission estimates are also only representative of emissions a few hours before the satellite overpass but not for the daily mean . It would therefore still be necessary to apply a correction factor to obtain the annual mean emissions, which introduces an additional source of uncertainty not included in our estimate. In our simulation, the emissions during overpass are about 18 % higher than the daily mean, suggesting that the sampling bias would be of the same order of magnitude. However, this result is entirely driven by the sector-specific diurnal emission cycles prescribed in the simulations. If the diurnal cycle of emissions was known from other sources of information such as traffic counts, electricity demand and heating statistics, a correction of the sampling bias could be applied, but this correction would add an additional uncertainty. The uncertainty in current estimates of diurnal emission variations is very poorly known, which makes it difficult to derive uncertainties in diurnal cycle or precise knowledge about ratios between different periods of the day . Studies such as those of , or all present diurnal emission cycles from various sources of information but no analysis of uncertainties. The diurnal cycles presented in these studies are roughly in line with our estimate of a sampling bias of the order of 20 % with respect to the daily mean. estimated uncertainties in the diurnal variation from uncertainties in activity data and emission factors, which, when applied to individual cities, would make it possible to better quantify the potential sampling bias in estimating annual emissions from sun-synchronous satellite observations in the future.

Finally, it should be noted that our results are representative for a city in mid-latitudes, where the temporal coverage is larger, as the satellites can pass over a city twice during the 11 d repeat cycle, whereas at the Equator only one satellite pass takes place per 11 d. The real temporal coverage is also strongly affected by the number of cloud-free observations in different latitudes.