Our approach to determine urban emissions is based on the differential column methodology . The column-integrated dry-air mole fractions of CO2, CH4, and carbon monoxide (CO) are measured with the help of at least two solar-tracking spectrometers that are placed upwind and downwind of an emission source. The concentration gradients between these stations represent the emissions that are generated in between. In Hamburg, the setup consists of four spectrometers to ensure that the differential column condition is met for most wind directions and that a meaningful background can be constrained by the inversion framework. As the wind direction is not constant throughout the measurement period, we placed four spectrometers in different locations around the harbor area where the highest emissions are expected according to the TNO GHGco inventory . The TNO GHGco inventory is an European database that includes spatially resolved emission data for CO2, CH4, CO, nitrogen oxides (NOx), and non-methane volatile organic compounds (NMVOCs). The spatial resolution is 1/60∘ for longitude and 1/120∘ for latitude, which represents an area of approximately 1.1 km × 0.6 km in Hamburg. The emissions are divided into 15 gridded nomenclature for reporting (GNFR) sectors. TNO GHGco is currently the highest-resolution GHG emission inventory that is available for Hamburg. For this study, yearly average emission estimates (as recorded in the inventory) were considered.

Between 27 July and 9 September 2021, our four FTIR spectrometers were measuring in Hamburg. From 30 July to 5 September, the instruments were deployed at the locations shown in Fig. . Before and after that, side-by-side measurements of the four spectrometers were carried out on a rooftop at the University of Hamburg to make sure that all instruments were properly calibrated to each other (see Fig. ).

The EM27/SUN instruments were deployed in custom enclosures that protected the spectrometer from rainfall and adverse weather conditions . These enclosures automatically open when the sun is visible, so that sunlight enters the spectrometer. When rainfall is detected, the system shuts its cover and the spectrometer is protected against precipitation. The instruments are connected to the internet, which enabled us to operate the four spectrometers remotely during a long campaign.

The enclosures were located to the west, south, and east of the center of Hamburg as well as in the center of the city, as visible in Fig. . The three sites outside of the city were selected in order to have little point source influence from local, near-by sources, and they were placed about 20 km from each other; therefore, the expected CH4 concentration gradients predicted by the inventory between the stations are well above the instrument precision. The northern site was co-located with the isotope measurements on the rooftop of the University of Hamburg Geomatikum building. This location was chosen by weighting different criteria: firstly, the availability of sites with suitable conditions to house a room-sized setup for isotopic measurements as well as the ability to set up of the FTIR instruments on top of a flat roof; secondly, the requirement for the site to be located outside of an industrial area – a high-emission zone according to the TNO GHGco inventory.

The retrieval of concentrations from interferograms was performed using GFIT GGG2014 according to . The measurements of the column-averaged dry-air mole fractions must be properly filtered to exclude measurement errors. In particular, these arise from nonoptimal solar tracking, which is mainly caused by clouds. We used two successive filtering steps. The first filtering step is based on physical properties, such as solar elevation, absolute solar intensity, and solar intensity variation, during a Michelson interferometer scan. The second filtering step uses data statistics to remove outliers and measurement periods with too few data points. In this step, measurements are split when no measurement is available for more than 18 s. Each 2 min section of data is then only considered when continuous measurement data exist for (at least) more than 1 min. This way, outliers from partial cloud coverage during the interferometer scan are reduced. Finally, the remaining continuous measurement sections are averaged using a 10 min moving average filter. Gaps are not filled.

In order to filter out days with fragmented and interrupted measurements due to repeated cloud cover, we only consider measurement days when at least two stations were measuring at the same time for more than 5 h. In August 2021, the weather was unexpectedly cloudy, and the systems were idle on many days; however, we still had 9 good measurement days with sufficient sunshine to carry out the measurements.

To support the modeling and the calculation of the final emission estimate, in situ measurements were performed with a Picarro GasScouter G4302, which measures CH4 and C2H6, and a Picarro G2301 greenhouse gas analyzer, which measures CH4 and CO2. Both sensors were mounted inside a car, and a tube was used to pipe the air from the inlet located on the front bumper into the sensors. The height of the inlet was ca. 60 cm above ground level. The CH4 concentration measurements, which were carried out with a sampling frequency of 1 and 0.3 Hz for the Picarro GasScouter G4302 and Picarro G2301 instruments, respectively, were temporally averaged using a moving average with a 10 s time window. The averaging improves the precision of the CH4 measurements from 3 ppb at a 1 s integration time to 1 ppb at a 10 s integration time .

In order to verify and update the prior estimate of an emission map derived from the TNO GHGco inventory , mobile surveys were conducted in the city and in the industrial area. The first part of the surveys focused on the residential areas of Hamburg, mostly to the north of the Elbe, and were conducted in the year 2018 by . In 2021, these existing measurements were complemented by a mobile survey with the same instruments in the industrial harbor area (​​​​​​​all tracks can be seen in Fig. ). The new survey took place between 9 and 21 August 2021. During the surveys, CH4, C2H6, and CO2 concentrations were recorded and mapped with a GPS logger. In order to cover the areas in the harbor that were not accessible by public road, a boat was equipped with the Picarro GasScouter G4302 and additional surveys were carried out on the Elbe River and the waterways in the harbor area on 20 August. Some private roads in the harbor areas were sampled after permission was granted from the facility owners, including a wastewater treatment plant and two refineries.

The recorded CH4 concentration during the mobile surveys was separated into its two components: the background and the enhancement peaks occurring near localized sources. While the background is generally rather smooth and varies only slowly with location, the short-time component (peaks in the signal) is caused by emissions from nearby sources. The background signal was determined as the lowest fifth percentile of a ±2.5 min time window around each data point. In order to compile an improved estimate of the spatial distribution of the emissions, both the complete signal (background and enhancement peaks, later referenced as “upd:all”) and the peaks only (later referenced as “upd:elv”) were averaged on the inventory grid, as can be seen in the right and central plots of Fig. .

The spatial distribution of emissions recorded in the original TNO GHGco inventory was then updated using the mobile concentration measurements. We assumed that it was more likely that we would find emission sources in regions where we measured high concentrations than in regions where we measured only background concentrations. The emissions of all inventory pixels that were covered by our mobile survey were summed up and distributed according to the measured concentrations, weighted by the number of measurements per pixel.

The following equations show how the original inventory E(x,y), a function of latitude x and longitude y, was updated using the concentration measurements C(x,y) averaged on the inventory grid. These measurements were either the whole signal (upd:all) or the peaks only (upd:elv).

First, the concentrations were normalized in the area where measurements were available, and the emissions recorded in the inventory were redistributed according to the measured concentrations. The new inventory values N(x,y) were calculated as follows: 1N(x,y)=C(x,y)∑x′,y′∈{C(x′,y′)≠NaN}C(x′,y′)∑x′,y′∈{C(x′,y′)≠NaN}E(x′,y′).

A weighting mask W(x,y) was then defined according to the number of measurements per pixel M(x,y): 2W(x,y)=M(x,y)max⁡x′,y′(M(x′,y′)).

New values were mixed between the original inventory value E(x,y) and the new values suggested by Eq. () according to the weighting mask W(x,y). In pixels with few measurement points, the new emission value of the pixel was chosen closer to the original value of the inventory. In pixels with many measurement points, the value was chosen closer to the value suggested by the concentration-based redistribution of emissions. 3Nmixed(x,y)=E(x,y)(1-W(x,y))+W(x,y)N(x,y)

The updated inventory Eupdated is then calculated depending on the availability of concentration measurements, as follows: 4Eupdated(x,y)=E(x,y),x,y∈{C(x,y)=NaN}Nmixed(x,y)∑x′,y′∈{C(x′,y′)≠NaN}Nmixed(x′,y′)×∑x′,y′∈{C(x′,y′)≠NaN}E(x′,y′),x,y∈{C(x,y)≠NaN}.

For a better comparability between the updated and the original inventory, the sum of emissions in the area covered by our mobile measurements is equal in the original and the updated versions.

The original TNO GHGco inventory has been created using proxy data. For example, all industry emissions reported by Germany were distributed on a map according to the distribution of industrial areas in Germany. In the three inventories used in our study, the industrial area south of the Elbe River has lower emissions in the updated versions than in the original inventory, as these emissions were distributed over a wider area according to the mobile measurements.

Furthermore, an inventory layer containing the Elbe and its estimated emissions was added. estimated the CH4 flux from the Elbe into the air for different sections of the river to be between 0.25 and 4.5 kg h-1 km-2. The emission values for the Elbe in each grid cell are the average flux of the corresponding section multiplied by the proportion of the Elbe inside the grid cell. For parts of the Elbe that were not covered in the study by , the average emissions of the study (2.5 kg h-1 km-2) were used as a prior estimate.

During the mobile survey carried out to map concentrations of CH4, multiple transects were undertaken through observed plumes. Plumes were manually selected when an enhancement higher than 100 ppb was observed. For each plume and location, between 3 and 15 transects were carried out. Sections in which the measurement car was immobile were removed before further analysis. Emission estimates were derived based on a Gaussian plume dispersion model (GPM), as described in . As the exact emission location was unknown for several sources, we calculated an estimate of the emission location for each transect. For this purpose, the possible Pasquill–Gifford stability classes were first estimated using wind sensor data, information on the planetary boundary layer height, and information on the surrounding area. In a next step, the width of the plume was used to derive σy. Under the assumption of a constant stability class, σy can be expressed as a function of the distance to the source. This function is independent of the flux, and thus an estimate for distance can be determined. The distance in combination with the wind direction lead to an estimate of the location for each transect. For each estimated source location, the flux is then estimated. Errors in the location estimates are propagated into the mean emission estimate. For each location, all relevant Pasquill stability classes were estimated. The presented mean emission estimates are the average of estimates obtained for each relevant stability class and location estimate.

During the transect drives that were carried out for emission quantification, wind information close to the ground was important. Therefore, a local portable wind sensor (Lufft WS200-UMB smart weather sensor), which measured wind direction and wind speed at an altitude of 2 m, was deployed.

To evaluate the uncertainty in the atmospheric transport of the ERA5 model inside the modeling domain, a Leosphere WINDCUBE 200S Doppler wind lidar was deployed at the weather mast in Billwerder, Hamburg (see Fig. ). The lidar provides a wind profile from approximately 80m to the top of the atmospheric boundary layer. Measured wind direction and wind speed were compared to the ERA5 model data for all altitudes where model and lidar data were available (see Fig. ). For each measurement day, the standard deviation of the differences between the ERA5 model and the lidar wind direction and speed were derived.

We took continuous measurements of CH4 at an inlet height of 80 m on the rooftop of the University of Hamburg Geomatikum building. Measurements started on 2 August and the setup was operational for most of the campaign period. It was shut down once for maintenance on 25 August and resumed operation on 27 August. We deployed an isotope ratio mass spectrometer (IRMS) that continuously measured δ13C and δD with a Delta V Plus and Deltaplus XL from Thermo Fisher Scientific .

In addition to the continuous measurements, air samples were taken at several locations while carrying out the mobile survey in order to characterize the source types of observed plumes, similar to .

To investigate the source mix of the measured CH4 and to decide whether it was mainly of thermogenic or biogenic origin, continuous analysis of the dual stable isotopic composition of CH4 (δ13C and δD) was performed, similar to previous studies . δ13C values are reported vs. the Vienna Pee Dee Belemnite (VPDB) standard, and δD values are reported vs. the Vienna Standard Mean Ocean Water (VSMOW) standard.

The dominant source type that is responsible for the observed CH4 elevations above background in Hamburg was obtained by comparing δD and δ13C values obtained from a Keeling plot analysis to similar sources signatures in the literature.

Sources were classified as biogenic when δ13C values were between -45 ‰ and -90 ‰ and δD values ranged from -245 ‰ to -360 ‰. In contrast, signatures with δ13C values between -32 ‰ and -67 ‰ and a δD value between -118 ‰ and -200 ‰ were attributed to thermogenic emissions .

In order to quantify the urban emissions based on the concentration measurements, a Bayesian inversion framework was used. We utilized and adapted the model as presented in according to the specific requirements of the Hamburg urban area.

This model was designed to quantify diffuse emission sources with the help of several ground-based spectrometers, such as the EM27/SUN. The model accounts for temporal variations in the background concentrations using the so-called background influence matrix (BIM). Analogous to their Supplement S1​​​​​​​, virtual particles are released along the line of sight according to the given solar azimuth and elevation angle at 13 altitudes up to 2220 m height above the instrument. These particles are released at the receptor time and travel backwards in time until they reach the simulation border (background time). A weighting factor is assigned to the times when the particles cross the border (background time), based on the number of particles passing the border at that time. This results in a nearly Gaussian-shaped distribution of background time for each receptor time. Every 15 min, such a release of particles from each receptor station is initiated. Releasing particles backwards in time is also the basis to generate footprint matrices, which represent the influence of all locations in the domain on the measurement site at a certain receptor time. The footprint is the summation of the residence time of all of the particles in a grid cell.

In order to generate those backward trajectories and the footprints, the STILT (Stochastic Time-Inverted Lagrangian Transport) model is used. The meteorological input data for this model were provided by the ERA5 data set .

The TNO GHGco inventory was used as a prior emission map . Additionally, the updated inventories that are depicted in Fig.  and described in Sect.  were compared.

Further assumptions for the model are a spatially homogeneous concentration at the modeling boundary (concentrations can vary with time) and a known spatial distribution of the diffuse emission sources provided by the inventory. The model minimizes a cost function to find the scaling factor for each emission sector that best fits the model to the measurements.

The cost function is described as follows: 5J(x)=12Kx-yTSε-1Kx-y+12xa-xTSa-1xa-x, where x is the unknown that needs to be fitted and that contains the information of the scaling factors for different emission sectors and the background concentration, K is the sensing matrix that contains the footprints' information and BIM, y is the column concentration measurements obtained from the four EM27/SUN instruments, xa is the prior emission information, and Sa and Sε are the prior error covariance matrices for the prior emission and data–model mismatch, respectively.

In this study, we use the existing framework developed by to estimate the emissions for individual days. The total emission estimate for the campaign period was calculated as the weighted average of the individual day results. The average was weighted by the number of measurement points per day. Negative emissions were considered when forming the average.

Emission estimates for smaller areas, such as the city of Hamburg or the northern part of Hamburg, were calculated by summing up the prior emissions from inventory pixels in that region. This sum was then multiplied by the inversion result (scaling factor) for all days from the respective inventory.

The error assessment follows the approach described in . The uncertainties are extracted from the posterior covariance matrix Sp, which is mathematically computed based on the sensing matrix K and the prior error covariance matrices Sε and Sa: 6Sp=KTSε-1K+Sa-1-1.

The uncertainty in the observations σobservationprior was chosen as the sum of the instrument precision, which is 0.2 ppb when the measurements are integrated over 10 min , and the transport error calculated for each day. The transport error was obtained by simulating a set of footprints for different wind directions. The wind directions were drawn from a normal distribution, with a standard deviation derived for each day by comparing the wind direction of the lidar and ERA5 model. No variations were made for the wind speed, as the mean mismatch between the lidar and model was as low as 0.49 m s-1. The resulting set of footprints was then multiplied by the three inventories used in this study to obtain a distribution of prior expected enhancements for all possible wind directions. The standard deviation of this distribution was used as the transport error. σobservationprior values are the diagonal elements of Sε.

The uncertainty in the prior emission map σsectorprior was chosen separately for the river layer and the layer with all anthropogenic sources. The river was given an uncertainty of ±200 %, whereas the anthropogenic sector was given an uncertainty of ±100 %. The uncertainty was higher for the river because a priori information was only available for a section of the river in and other areas were estimated with a mean flux of 2.5 kg h-1 km-2. The uncertainty in the background σbackgroundprior was chosen to be 8 ppb, slightly below the value of 10 ppb used by , according to a comparison of MUCCnet measurements with the Copernicus Atmosphere Monitoring Service (CAMS) data. σsectorprior and σbackgroundprior are the diagonal elements of Sa, as in .

The model mismatch for wind direction and wind speed was calculated for the selected measurement days by comparing lidar data and ERA5 model data. Table  shows that the wind speed is generally matched well by the model. A mean difference of 0.49 m s-1 between the model and lidar was recorded (i.e., the lidar recorded a slightly faster wind speed on average). The wind direction is off by an average of 6.0∘.

The calculated mismatch was considered when calculating the transport error for each day, as recorded in Table . These daily transport error values were then considered in the inversion framework.

During the campaign period, there was a good agreement between the modeled and measured planetary boundary height, as can be seen in Fig. .

A comparison of wind data from the local sensor (at 2 m altitude) used for the GPM emission estimates and the weather mast (at 10 m altitude) showed a mean difference of 1.6 m s-1 (standard deviation of the difference was 1.2 m s-1) for the wind speed and a mean difference of 15∘ CW​​​​​​​ (standard deviation of 31∘ CW) for the wind direction.

In Fig. , the measured concentrations as well as the modeled signal and background are shown for each day. The corresponding emission estimates for the original inventory and the two updated inventory versions are shown in Fig. .

On 2 respective days, 23 August and 3 September, while the stations were measuring simultaneously, little enhancement (< 2 ppb) between the stations was observed for most of the time. This is visible from the measurements of the different spectrometers (plotted as colored dots) in Fig. . Small enhancements result in low emission estimates for these days, as can be seen by comparing Figs.  and .

On other days, in general, larger enhancements between the stations were observed, resulting in larger emission estimates. The 6, 11, 12, and 24 August all show emission estimates higher than or equal to the prior. The 1 and 5 September have been estimated at values between the prior and zero emissions.

Looking at the result for 12 August in Fig. , it becomes evident that the North (me) spectrometer measured a peak at around 12:00–13:00 UTC; this peak was not measured by the other stations. During the time of the peak, the wind did not change direction and was constantly blowing from the south. Thus, the prominent elevation indicates the presence of an unknown temporary source. The inversion framework assigns this elevation to an enhancement of the background concentration (dashed black line at around 10:15 UTC) to balance out observations and prior expected contributions.

On 31 August, the West (mc) spectrometer, which was located about 1.5 km south of the Elbe River, measured an enhancement of about 5 ppb compared with the other stations throughout the whole day, as can be seen in Fig. a. During the course of this day, the wind came from the north, as can be seen by looking at the footprints visualized in white and blue on top of the TNO GHGco inventory in Fig. b.

With the original inventory, the inversion cannot model the enhancement seen by the West (mc) station, as there is no large source in the inventory north of the spectrometer. In such a case, the modeled signal, visualized using solid lines in Fig. a, does not match the actual measurements (dots) very well. The difference is visible, for instance, by looking at the distance between the purple line (the West (mc) station) and the purple dots in Fig. . In such a case, the modeled background at the domain boundary (dashed black line) is fitted higher than the signal (solid lines). This can result in negative emission numbers (Fig. c), as the enhancement (measurements - background) becomes negative for most time steps.

When the Elbe River is included in the emission inventory as quantified by , the modeled signal fits the measurements better and the inversion result returns positive emissions. On this particular day, the emissions of the Elbe were quantified as being much higher than the a priori annual emissions of the Elbe in our domain (350 kg h-1). Thus, for consistency, we decided to include the Elbe River in all other model runs and days presented in this paper. On other days, the emissions from the Elbe were close to the prior estimate or around zero, as can be seen in Fig. .

The expected contributions from different sectors for the 31 August are shown in Fig. . These expected contributions were calculated using the footprint and the inventory. As can be seen, the West (mc) station was sensitive to river emissions on 31 August. Moreover, the West (mc) station was sensitive to river emissions on 23 and 24 August as well as on 5 September. On all of these days, the concentrations measured by the West (mc) station were generally higher than those measured by other stations (see Fig. ).

For the selected days, the correlation between modeled and measured CH4 concentrations was very high for the total signal (modeled background + enhancement), as can be seen in Fig. a. Figure b shows the correlation for the enhancement only. Modeled enhancements were divided into 0.5 ppb bins, and sample means of the first bin (0–0.5 ppb) and the all other bins are significantly distinct (p=0.001), demonstrating the quantification of small and large enhancements in total column CH4 .

The correlation increased significantly when including the natural source into the modeling, as is visible in Fig.  in the Appendix.

In this study, three different versions of the emission inventory have been used as a prior estimate for the spatial distribution of CH4 emissions in Hamburg. While all three versions lead to comparable results for all measurement days combined, the results differ significantly on single days, as can be seen in Fig. . Over the course of all 9 d, the footprint has covered almost all of the areas of the modeling domain (because of different wind directions throughout the campaign), whereas only small parts of the domain are covered on single days.

The difference in emission estimates for the three inventory versions on single days can be explained by the different spatial distributions of prior emissions. In the area covered by the footprint on a particular day, the recorded emissions can be different in the original and the updated inventories. These differences in prior emissions for each inventory version lead to different scaling factors with the same observations. The scaling factor is determined by the inversion when scaling the three inventory versions to match the forward model and the observations. As all emission inventories are normalized and have the same total emissions, a different scaling factor applied to the whole inventory can then lead to different total emission estimates.

For instance, the inversion result can differ between the original and the modified inventories when there is footprint covering the industrial zone of the inventory. This zone has higher emissions in the original inventory than in the two updated versions, as visible in the lower left panel of each inventory in Fig. . With the same observations, the scaling factor calculated by the inversion framework will be slightly lower with the original inventory, as the inventory already has higher emissions recorded here, and higher with the updated inventories, as the updated inventories have lower emissions recorded here. For all days, the area covered by the measurement footprints encompasses the domain more uniformly; thus, a result in a similar magnitude can be expected for all inventory versions.

We ran the inversion for all inventories (original, upd:all, and upd:elv) with the Elbe River as a separate sector. Therefore, the emissions are split between river emissions (natural) and anthropogenic sources. We determined the emissions for the entire modeling domain as well as for the area inside the municipality border of Hamburg. The extent of the modeling domain and the area considered to be the city can be seen in Fig. .

The emission rate estimates for natural and anthropogenic sources combined in our modeling domain sum to 6300 ± 3500 kg h-1 for the original inventory, 6300 ± 4100 kg h-1 for the updated inventory using peaks and background (upd:all), and 5800 ± 4500 kg h-1 for the updated inventory using peaks only (upd:elv) (see Table ). A total of 1900 ± 1000 kg h-1 of these emissions was attributed to a natural source spanning the whole modeling domain (potentially the Elbe River and associated wetlands).

For the municipal area of Hamburg (including the river, the port, and industrial and residential zones), the sum of natural and anthropogenic CH4 emissions estimated by this study ranges from 1500 ± 1200 to 1600 ± 920 kg h-1. The CH4 emissions from natural processes for the Hamburg area were estimated to be 730 ± 410 kg h-1; thus, the emission from anthropogenic sources are estimated to be around 900 ± 510 kg h-1 (for the original prior).

When we split anthropogenic emissions in Hamburg into biogenic emissions and emissions of thermogenic origin according to the split in the TNO GHGco inventory (see Table ), 480 ± 260 kg h-1 of the emissions is attributed to thermogenic sources and 420 ± 240 kg h-1 is attributed to an anthropogenic biogenic origin, such as wastewater or landfills (see Fig. ).

If we only look at the part of Hamburg that is located north of the Elbe, which was also studied by , our emission estimate is 420 ± 230 kg h-1 for anthropogenic sources. This is higher than the 46 ± 8.0 kg h-1 reported by in their study based on upscaling emissions from a mobile CH4 survey with a car. The difference can be partly explained by the different scientific objectives (and thus methodologies) used in both studies. While our study targeted total emission quantification (i.e., from all sources) using column instruments and, thus, can also capture sources that are emitting above the street level, the in situ measurements carried out by were used to specifically target ground-level emissions near public roads, including the identification and quantification of fugitive emissions from gas pipeline leaks and the sewer system (not including the wastewater treatment plant). If we consider only fugitive emissions according to the TNO split (Table ), our study estimates emissions of 210 ± 110 kg h-1 for the northern part of Hamburg. This is between 2 and 8 times higher than the estimate presented by . One potential source that is usually not measurable at the street level, and could thus explain the lower emissions measured by , is end use inside homes (e.g., cook stoves and boilers for heating) . Accumulated emissions from end use, while not affecting street-level concentrations, could be observable in total column measurements and, thus, contribute to the higher emission estimates of this study. Other potential sources in Hamburg that could possibly contribute to higher column-measurement-based estimates are the Alster lakes near the city center. detected CH4 enhancements that were low in magnitude but spread over a large area around these lakes. These low enhancements could not be used for quantification and are, thus, not included in their estimate, but they might be noticeable in the column measurements.

For several locations inside the study area, emission estimates were derived using a GPM from transects recorded during the mobile survey. All transects for each location were undertaken on the same day. These estimates are presented in Table  and are compared to the emissions recorded in the TNO GHGco inventory as well as the two updated versions. While the emissions of the two updated inventory versions were only spatially redistributed according to the recorded spatial distribution of CH4 concentrations, the GPM emission estimates consider wind information to obtain emission estimates.

For location 1, an oil refinery, sample bags were analyzed and an isotopic signature of thermogenic CH4 emissions was detected. These emissions were quantified as 7.9 ± 5.3 kg h-1 by driving multiple transects around the source location, as visualized in Fig. . This value is significantly larger than the value (0.61 kg h-1) recorded in the TNO GHGco inventory for thermogenic CH4 emissions in the corresponding pixel. Moreover, there is no source recorded in the European Pollutant Release and Transfer Register (E-PRTR; ), which suggests that it is an unknown source. The updated version of the inventory upd:all, with a value of 6.4 kg h-1, is closest to the Gaussian plume emission estimate for the corresponding inventory pixel. The updated inventory version upd:elv suggests even higher emissions for that pixel (76 kg h-1). The fact that the source at location 1 was observed on several measurement days (and had also already been observed during the measurements in 2018) suggests that this source could have been emitting continuously for a longer time.

At location 2 north of the Elbe, the industrial area, and north of the municipal wastewater plant, transects were carried out, and an emission estimate was derived from the measured plumes, as shown in Fig. . This estimate of 6.7 ± 13 kg h-1 has a high relative uncertainty because the estimated source location was far away from the transect lines. The GPM estimate is not significantly different from the values reported in the original and two updated inventory versions (5.4, 15, and 19 kg h-1, respectively). Emissions for this location were estimated during a period with southerly wind directions; thus, they could have originated from various sources within the industrial area as well as from the wastewater treatment plant. At this location, no samples were taken because plumes were not always stable.

Location 3 is situated in the industrial complex south of the Elbe near harbor water ways and adjoining several ports used to load or fill boats with gas- and oil-derived products (see Fig. ). For this location, several large plumes were observed at the site of a refinery. These were attributed to thermogenic and biogenic source signatures. Biogenic sources, however, turned out to be dominant in a Keeling analysis of the sample bags. Biogenic emissions could have originated from near the waterbody or from the fermentation of wastewater from the facility. The estimated emissions from this location are 3.1 ± 2.3 kg h-1, which confirms the value recorded in the corresponding TNO GHGco inventory pixel (4.0 kg h-1). The updated inventory version “upd:all” (4.6 kg h-1) is not significantly different from the GPM estimate, whereas the value in the upd:elv version is significantly higher (40 kg h-1).

The transects at location 4 were undertaken on the private roads of a refinery after permission was granted from the operator. The first drives were distributed around the accessible area of the refinery, and they were then narrowed down to locations where plumes were detected. The emissions of a prominent point source, present during the time of the survey, were quantified as being 1.1 ± 0.7 kg h-1, which confirms the values recorded in the TNO GHGco inventory and the updated versions (as can be seen in Table ).

At location 5, plumes were detected downwind of two large sheds situated on a farm near Meckelfeld. Isotope measurements of air samples collected at this location indicated a biogenic source origin. For this source, the upd:elv inventory provides the closest estimate of 3.8 kg h-1. The GPM estimate of 8.4 ± 2.5 kg h-1 is considerably higher than the values recorded in the original and the upd:all version of the inventory (0.55 and 0.87 kg h-1, respectively).

Transects at locations 6 and 7 were both carried out by boat. Two point sources with respective magnitudes of 6.6 ± 13 and 4.5 ± 4.4 kg h-1 were found in the industrial area. No sample bags were analyzed for these locations. For both locations, the original inventory is closest to the emission estimate; however, the difference between the updated and original inventories is small. Both estimates have a high relative uncertainty, as only very few transects were available and the estimated source location could possibly be too far from the transects. Both GPM estimates are not significantly different from the values recorded in the original and updated inventory versions.

In general, several significant CH4 sources were quantified during the mobile survey. While several GPM estimates confirmed the values recorded in the emission inventory (both the updated and original versions), some of the biogenic and thermogenic sources estimated using GPM, like locations 1 and 5, were significantly above the values recorded in the TNO GHGco inventory. The correlation between GPM estimates and the inventory values is highest for the upd:elv inventory: R2 = 0.13 compared with R2 = 0.10 and R2 = 0.10 for the upd:all and the original inventory, respectively. On the other hand, the root-mean-square error (RMSE) is highest for the upd:elv inventory: 27 kg h-1 compared with the upd:all and the original inventory with a RMSE of 4.4 and 4.1 kg h-1, respectively.

The emissions from anthropogenic activity in the city of Hamburg were estimated to be 900 ± 510 kg h-1, which is not significantly different from the 1400 kg h-1 reported in the TNO GHGco inventory for the year 2015.

During our study, we observed influence from a biogenic source, which was modeled as river emissions. Large natural area sources such as waterbodies were previously not recorded in the TNO GHGco inventory.

The column-measurement-based CH4 emission estimates for all sectors (natural and anthropogenic sources) in the whole domain, covering the city of Hamburg and parts of the surrounding land outside of Hamburg, are of the same magnitude as those reported by inventories, as can be seen in Fig. .

The stationary in situ measurements on the rooftop of the Geomatikum building (University of Hamburg) show numerous concentration peaks with enhancements of around 1–2 ppm, as visible in Figs.  and . During the campaign, these peaks were only measured during the night or when the column instrument was not measuring due to cloud cover. Both δ13C and δD Keeling plots yield source signatures that indicate a biogenic origin (δ13C -61.5 ‰ ± 0.3 ‰ and δD = -320 ‰ ± 2.5 ‰) for these peaks, as can be seen in Fig. . Potential sources that generally have a similar signature are microbial in nature . Both agricultural sources, such as cattle , and waste have overlapping signatures with the unknown source in Hamburg. found a similar signature (δ13C −66.1 ‰ and δD = −310 ‰) for air in a subway station. A study on a river estuary at the border between Belgium and the Netherlands by found a comparable signature for δ13C (between -25.2 ‰ and -65.6 ‰) but a more enriched signature for δD (between +101 ‰ and -212 ‰). δD signatures of as low as -260 ‰ have been measured by for gassy sediments in an estuary in Germany. The slightly more depleted δD signature measured in this study suggests that the unknown source in Hamburg could be a mix of several different biogenic (microbial) sources. One of these could be a large natural CH4 source, such as the river or wetlands, that emits in Hamburg (see also Sect. ). However, the river flow in the city area is also influenced by anthropogenic activity (e.g., harbor traffic and wastewater) which could contribute to lower δD values. The sharp short-term peaks could be caused by canals in the city close to the in situ instrument; these fall dry during low tide and then fill up again during high tide. This hypothesis is supported by the temporal correlation of CH4 peaks with the rising tide, as visible in Fig. . Furthermore, less-pronounced peaks, such as those in the early morning on 20 August, 31 August, and 2 September, follow this pattern.