The measurement campaign used for comparison with WRF-GHG in this paper was performed from 23 June to 11 July 2014 in Berlin using five spectrometers . It allows us to both test the precision of WRF-GHG (Sect. ) and verify differential column methodology (DCM) as our analytic methodology (Sect. ). In their measurement campaign, used five portable Bruker EM27/SUN FTSs for atmospheric measurements based on solar absorption spectroscopy. Five sampling stations around Berlin were set up, four of which (Mahlsdorf, Heiligensee, Lindenberg and Lichtenrade) were roughly situated along a circle with a radius of 12 km around the center of Berlin. Another sampling site was closer to the city center and located inside the Berlin motorway ring at Charlottenburg (Fig. ). Detailed information on this measurement campaign is given in , and provide additional details on the calibration of the spectrometers, precision and instrument-to-instrument biases.

Winds have a strong impact on the vertical mixing of GHGs and a direct influence on their atmospheric transport patterns. Hence, we firstly compare the wind speeds and wind directions obtained from WRF-GHG to the measurements such that deviations between the simulated and measured wind fields are assessed. The wind measurements are not exactly co-located with the spectrometers mentioned in Sect. 3.1, but are rather located at three sampling sites (Tegel, Schönefeld and Tempelhof) and measure at a height of 10 m above the ground. The simulated wind speed at 10 m (ws10m) and wind direction at 10 m (wd10m) are calculated following the equations 2ws10m=u10m2+v10m2,wd10m=arctan⁡v10mu10m, where u10m and v10m are the components of the horizontal wind, towards the east and north, respectively, which can be obtained from WRF-GHG output files.

Figure  shows the comparisons of wind speeds (Fig. a) and wind directions (Fig. b) between simulations and observations at 10 m from 1 to 10 July and the model–measurement differences. EM27/SUN only operates in the daytime when there is sufficient sunlight; the detailed description of the instrument can be found in , and . The instrumental working periods are marked by gray shaded boxes in Fig. . The measured (dashed lines) and simulated (solid) wind speeds (Fig. a) at 10 m show similar trends and demonstrate relatively good agreement over the 10 d time series, with a root-mean-square error (RMSE) of 0.9247 m s-1. Large uncertainties in wind speeds are found to appear always with the lower wind speeds, mostly at night. In terms of wind directions at 10 m, we observe that the simulated wind directions show similar but slightly underestimated fluctuations (Fig. b), which result in an RMSE of 60.8328∘. Larger uncertainties in wind directions always exist during the low wind speed periods (Fig. a, b). During the instrumental working period (within the daytime), the simulations fit better with the measurements with relatively lower RMSEs of 0.6928 m s-1 for wind speeds and 41.4793∘ for wind directions. We find that the measured wind fields (both wind speeds and wind directions) have more fluctuations compared to the simulations. This could be caused by really fast wind changes which the model, simulating a somewhat idealized environment, is not able to capture. To be specific, local turbulence given by urban canopy, buildings, etc., is not represented well in the model.

In the following, we use the measured concentration fields to compare with the simulated fields. An FTS EM27/SUN can measure the column-integrated amount of a tracer through the atmospheric column with excellent precision, yielding the column-averaged dry-air mole fractions (DMFs) of the target gases (). The measured DMFs of CO2 and CH4 are denoted by XCO2 and XCH4. used constant a priori profile shapes in the retrievals of measurements.

When comparing remote sensing observations to model data (or also datasets from different remote sensing instruments to one another), limitations of the instruments in reconstructing the actual atmospheric state need to be taken into account. In general, this requires the a priori profile that is used for the retrieval and the averaging kernel matrix, which specifies the loss of vertical resolution (fine vertical details of the actual trace gas profile cannot be resolved) and limited sensitivity (e.g., ). In the case of EM27/SUN, the spectrometers used in the network offer only a low spectral resolution of 0.5 cm-1. Therefore, performing a simple least-squares fit by scaling retrieval of the a priori profile is generally appropriate. In this case, there is no need to specify a full averaging kernel matrix; instead, the specification of a total column sensitivity is sufficient. The total column sensitivity is a vector (being a function of altitude), which specifies to which degree an excess partial column superimposed on the actual profile at a certain input altitude is reflected in the retrieved total column amount. This sensitivity vector is a function of a solar zenith angle (SZA; and ground pressure), mainly due to the fact that the observed signal levels in different channels building the spectral scene used for the retrieval are shaped by a mixture of weaker and stronger absorptions. (If all spectral lines in the spectral scene are optically thin and too narrow to be resolved by the spectral measurement, the sensitivity would approach unity throughout.)

In order to ensure measurement quality and enough sample points for further concentration comparisons, we select five measurement dates (1, 3, 4, 6 and 10 July) with relatively good measurement qualities (from fair, “++”, to very good, “++++”) based on . The pressure-dependent column sensitivities for CO2 (Fig. b) and CH4 (Fig. c) are derived from measurements performed in Lindenberg on 4 July (the best-quality day in terms of measurements). Details about the measurements can be found in and . The shape and values of the column sensitivities from Lindenberg in Berlin closely resemble the results of in Pasadena. As depicted in Fig. a, the SZAs are almost identical for each day in our study (at each hour), rendering the shape of column sensitivities (at a specific hour of the day) practically independent of the measurement date. The column sensitivities for 4 July (Fig. b, c) are taken as a basis for our smoothing process below. The a priori CO2 and CH4 profiles have been taken from the Whole Atmosphere Community Climate Model (WACCM) version 6. A smoothed profile for a target gas G is then obtained as in Eq. (3) in , 3Gs=K⋅G+(I-K)⋅Gp, where G is the modeled profile from WRF-GHG, I is the identity matrix, K is a diagonal matrix containing the averaging kernel and Gp is the a priori profile.

In order to compare the simulated smoothed concentration fields with the observations, the simulated smoothed pressure-weighted column-averaged concentration for a target gas G (XG) is calculated as 4Δp(i)=P(i)-P(i+1)Psf-Ptop→XG=∑i=1nΔp(i)×Gs(i). Here, Δpi is proportional to the differences of the pressure values P(i) at the bottom and P(i+1) at the top of the ith vertical grid cell, Ptop and Psf represent the hydrostatic pressures at the top and at the surface of the model domain, and Gs(i) stands for the simulated concentration of the target gas G at the ith vertical level.

In Figs.  and  of Appendix D, we compare the simulated XCO2 and XCH4 with and without smoothing. The simulated concentrations are only slightly enlarged after smoothing, at approximately 1–2 ppm for XCO2 and 2 ppb for XCH4, while the variations are mostly unchanged. Compared to the period with lower SZAs (at noon), the smoothed values in the morning and afternoon with higher SZAs hold relatively larger enlargements.

Figure a shows the measured and smoothed modeled variations in XCO2 and XCH4 for these 5 d. Compared to the measurements, the smoothed simulated pressure-weighted column-averaged concentrations for CO2 (XCO2) show quite similar trends but with approximately 1–2 ppm bias, indicated by an RMSE of 1.2534 ppm. The simulated XCO2 values are overestimated for 1, 3 and 4 July, while on 6 and 10 July, the model is underestimated, which could be the result of uncertainties from the coarse anthropogenic surface emission fluxes, background concentrations from CAMS and the ignorance of the influence from the line of sight of the sun.

Figure b shows the comparison of the pressure-weighted column-averaged concentrations for CH4 (XCH4) between observations and smoothed simulations on the five selected dates (1, 3, 4, 6 and 10 July). We find that there is an approximate offset of 50–60 ppb between observations and models (RMSE is 58.1082 ppb). The simulated XCH4 is around 1860 ppb while the measured value is around 1810 ppb, which is comparable to the values (1790–1810 ppb) observed at two Total Carbon Column Observing Network (TCCON) measurement sites in June and July 2014 in Bremen in Germany and Bialystok in Poland . This bias of the simulated XCH4 seems to be constant (around 2.7 %) each day. Thus, we introduce an offset applied to all sites for each simulation date to compare the model and the measured data, effectively removing the bias, which we attribute to too high a background XCH4. The daily offset is assumed to be the difference between the smoothed simulated and measured daily mean XCH4. After applying the daily offset, the measured XCH4 shows a somewhat better agreement and a similar trend but with larger variability compared to the simulation (RMSE is 3.1690 ppb). The smaller variations from the simulation results can, for example, be caused by the error from the spatio-temporal treatment of emission maps, underestimated emissions from anthropogenic activities, the coarse wind data and/or the smoothing of actual extreme values in the simulation.

A major offset in modeled CH4 concentration fields could potentially be attributed to the errors in the troposphere height and a general offset from CAMS. In the CH4 vertical concentration profile, we find that the typical sharp decrease occurs at the tropopause height. also find the similar sharp decrease when using the AirCore to retrieve atmospheric CH4 profiles in Finland. During the simulation, the background concentration values of CAMS are directly fitted to the WRF pressure axis without considering the actual tropopause height; thus this could cause some error. An illustration of the vertical distribution for CH4 is provided in Appendix C. In contrast, the CO2 vertical distribution shows decrease that is quite flat with the increase in pressure, and there is no need to consider the tropopause height during the grid treatment in the vertical layer. In terms of CAMS, the reports from Monitoring Atmospheric Composition and Climate (MACC) stated that CAMS has a bias and RMSE (approximately 50 ppb) in each part of the world, compared to the Integrated Carbon Observation System (ICOS) observations in 2017 . also mentioned one CH4 offset (approximately 30 ppb within troposphere) when initializing the concentration fields using CAMS. Apart from these two major potential reasons for the bias, the influence from the inaccurate simulated planetary boundary layers and the shape of the constant a priori profile used for the retrievals could both potentially contribute to the discrepancies for the concentration fields. Due to the lack of fine measured vertical concentration profiles, it is not easy to quantify these errors and attribute these potential reasons to this 2.7 % error quantitatively. Thus, a DCM-based analysis is presented in Sect. , aiming at eliminating the bias from these relatively high initialization values for CH4 and making it easier to assess WRF-GHG results with respect to the measurements.

As described in Sect. , the various flux models implemented in WRF-GHG are advected as separate tracers, making it possible to distinguish the signals in concentration space for different source and sink categories for CO2 and CH4 . Berlin is located in an area of low-lying, marshy woodlands with a mainly flat topography . There is no wetland in Berlin according to the MODIS Land Cover Map . The land covered by forests, green and open spaces (e.g., farmlands, parks and allotment gardens) accounts for 35 % of the total area in Berlin . Additionally, 11 power plants are currently being operated in Berlin, 8 of which have a capacity of over 100 MW . In accordance with the geographical characteristics of the district and potential emission sources in Berlin, we focus on understanding the major emissions caused by vegetation photosynthesis and respiration (XCO2,VPRM) as well as anthropogenic activities (XCO2,anthro) for CO2 and by soil uptake (XCH4,soil) as well as human activities (XCH4,anthro) for CH4.

As an instructive example of an analysis involving these tracers, we look at the diurnal cycle of contributions from the different tracers mentioned above in Charlottenburg (Fig. ). The mean values, averaged over 9 d (from 2 to 10 July), as well as a 95 % confidential interval calculated in the averaging process are shown in Fig. . Figure a clearly shows a decline during the day and a rise at night in the XCO2 enhancement over the background (blue: XCO2,total – XCO2,bgd), with a maximum decrease over the course of the day of around 2 ppm. The XCO2 enhancement over the background reaches its daily peak during morning rush hour (07:00 UTC). The morning peak corresponds to XCO2 changes from human activities, depicted by the black line from 04:00 to 07:00 UTC (marked by a red square in Fig. a). Before the evening rush hour (16:00 UTC), XCO2 over the background then decreases, owning to biogenic uptake. Beginning in the evening, values increase again. The fluctuation in the evening (17:00–19:00 UTC) is dominated by XCO2 enhancements from human activities, while the substantial rise from 19:00 UTC onward is generated by the VPRM tracer, specifically the accumulation of the vegetation respiration in the evening.

XCO2 is weaker compared to the strong biogenic uptake. To further highlight the role of anthropogenic activities in XCO2 changes within the urban area, DCM is applied in Sect. . More specifically, we will use downwind-minus-upwind column differences of CO2 (ΔXCO2) to describe the XCO2 enhancement over an upwind site, as the difference between the downwind and upwind sites can be attributed to urban emissions.

Turning to XCH4 in Fig. b, we plot the variations in the mean hourly contributions from the anthropogenic (black line: XCH4,anthro) and soil uptake tracer (blue line: XCH4,soil) in Charlottenburg. The contributions by anthropogenic activities fluctuate slightly around 2 ppb in the morning and at noon; then a peak occurs at the start of the evening rush hour (16:00 UTC). After 18:00 UTC, values clearly decrease, reaching approximately 2 ppb. From 21:00 UTC, XCH4 stabilizes, exhibiting only moderate fluctuations. The XCH4 enhancement above the background (green: XCH4,total-XCH4,bgd) depends largely on the XCH4 contributions by human activities. The changes in concentrations caused by the soil uptake tracer (blue), whose values fluctuate between 0.001 and 0.01 ppb, have almost no influence on the variation in the XCH4 enhancement over the background in the urban area.

The DCM can be employed to detect and estimate local emission sources within an area, based on calculated concentration differences between downwind and upwind sites . The difference (ΔXG) of a specific gas G in column-averaged DMFs across the downwind and upwind sites is defined as 5ΔXG=XGdownwind-XGupwind, where XGdownwind and XGupwind represent the column-average DMFs at the downwind and upwind sites.

In this study, DCM is applied to measurements and models in the spirit of a post-processing analysis. This approach is not only useful for canceling out the bias of the simulated XCH4 (see Sect. 3.3) but also for assessing the role of anthropogenic activities in XCO2 changes more appropriately.

A necessary prerequisite for DCM is distinguishing the upwind and downwind sites among all five sampling sites. Wind direction thus plays a pivotal role in the calculation of the downwind-minus-upwind column differences. In this study, the hourly simulated vertically averaged wind directions are assumed as a standard to classify the sites into downwind and upwind sites. The tracer transport calculations in the first few hours are not stable in WRF-GHG. Thus, we select 3, 4, 6 and 10 July as our targeted dates.

Table 1 shows the daily averaged wind directions with standard derivations and the details on the downwind and upwind sites for these four target dates. West wind is the prevailing wind direction on 3 July. That is to say, Mahlsdorf and Lindenberg are downwind sites, and the upwind sites corresponding to these are Charlottenburg and Heiligensee, described in Eq. (6). The wind on 10 July is northeasterly, and the combination of downwind and upwind sites are selected to be opposite of the ones on 3 July, see Eq. (8). The prevailing winds on 4 and 6 July are easterly. The upwind site is Lichtenrade, and the corresponding downwind sites are Heiligensee and Lindenberg, see Eq. (7). Based on the selection of downwind and upwind sites shown in Table 1 and Eq. (5), differential column concentrations (ΔXCH4) are, therefore, calculated as 6Western wind (3 July):ΔXCH4=(XCH4Mahlsdorf+XCH4Lindenberg)/2-(XCH4Charlottenburg+XCH4Heiligensee)/2.7Northern wind (4 and 6 July):ΔXCH4=(XCH4Heiligensee+XCH4Lindenberg)/2-XCH4Lichtenrade.8Northeastern wind (10 July):ΔXCH4=(XCH4Charlottenburg+XCH4Heiligensee)/2-(XCH4Mahlsdorf+XCH4Lindenberg)/2. Figure  depicts the variations in the wind fields (wind speeds and wind directions) and ΔXCH4 (corresponding to Eqs. 6, 7 and 8) on 3, 4, 6 and 10 July. As depicted in the Fig. a–d, the hourly vertically averaged simulated wind speeds and directions at downwind and upwind sites are homogeneous. Thus, it is reasonable to use the daily mean wind directions as the standard for the selection of downwind and upwind sites. The general trends in the simulated ΔXCH4 values, shown in Fig. e–h, seem to be roughly reproduced by the observations but slightly overestimated, with an RMSE of 1.3895 ppb.

Yet DCM as presented here has the potential to highlight the role of anthropogenic activities, which we demonstrate, applying it to CO2 tracers in the simulation. Thus, the analysis on anthropogenic and biogenic tracers for CO2 will be especially prominent here. As described above, we continue to take 3, 4, 6 and 10 July as examples (see Fig. a–d).

The variations in ΔXCO2 (corresponding to Eqs. 6, 7 and 8) on 3, 4, 6 and 10 July are shown. In contrast to the variations in XCO2 values (Sect. 3.4; Fig. a), the simulated ΔXCO2 (Fig. a–d, blue lines) is not so much influenced by the XCO2 changes from the VPRM tracer (Fig. a–d, green) but more closely follows the XCO2 changes from anthropogenic activities (Fig. a–d, red). With DCM, the role of human activities in XCO2 changes is highlighted, and the strong effect from the biogenic component is canceled out. The ΔXCO2 measurements (Fig. a–d, black) show similar trends as the simulation with an RMSE of 0.2973 ppm.

To further understand the differences of ΔXCO2 and ΔXCH4 between measurements and simulations (see Fig. e–h and Fig. a–d), the comparison of hourly mean ΔXCO2 and ΔXCH4 values for these four targeted dates is illustrated in the right column of Fig. . Due to the restriction of measured wind information, we illustrate the differences of simulated and measured wind directions at 10 m (i.e., Fig. b) with respect to the hourly mean ΔXCO2 and ΔXCH4. We find that the real hourly mean ΔXCO2 and ΔXCH4 values are generally higher than the simulated values. Extreme points are colored by red and blue in the right column of Fig. e–f, standing for large differences between measured and simulated wind directions at 10 m. We see that a large difference of wind directions is a necessary but insufficient condition for the bias of ΔXCO2 and ΔXCH4 between measurements and simulations. In future studies, this is suggested as something to be verified further.

We conclude that DCM, as applied in this plot, reduces the model bias caused by the simulation initialization but introduces unpleasant effects which may be attributed to errors in the assumed or simulated wind directions.

As described in Sect. 4.1, the wind direction impacts the distinction between downwind and upwind sites for DCM. Devising meaningful and accurate recipes for determining the wind directions is not easy, sometimes resulting in mixed-quality results (of Sect. 4.1). Our simulated output provides the hourly wind and concentration fields. The instruments measure the concentration value every minute . We simply assume the wind direction to be a constant value within 1 h (the hourly vertically averaged values) in our calculation also when it comes to selecting upwind and downwind sites. This may create inaccuracies in the calculation of the measured ΔXCH4.

In this section, we test replacing the upwind values in DCM by an all-site mean to provide a potential solution for the elimination of such problems while still applying the DCM. The mean of the column-averaged DMFs over all sampling sites (XG‾specific site) is assumed to be the background concentration within the entire urban region, replacing the XCH4 at the upwind site. The differences between the specific site and the mean of all the sites for each gas G (ΔXG‾specific site) is then evaluated, i.e., 9ΔXG‾specific site=XGspecific site-XG‾all sites, where XGspecific site is the column-averaged DMF at the respective sampling site.

We now test this form of DCM for the same four targeted dates (3, 4, 6 and 10 July). The distance between any two sampling sites is around 25 km. The general trends of the simulated (Fig. , blue lines) and measured (Fig. , black lines) ΔXCH4‾ values appear to be more similar with an RMSE of 0.6698 ppb compared to the comparison of ΔXCH4 in Fig. e–h (RMSE of 1.3895 ppb). The model–measurement bias can be caused by underestimated emissions from anthropogenic activities, the smoothing of actual extreme values in the simulation and the ignorance of the line of the sun sight for the simulation. The variations in the XCH4 at the five different sampling sites on the same day are similar (Fig. ), but the measurements show more extreme values (e.g., 4 July) compared to the simulations. A further analysis in a future study is suggested to provide deeper insight into site-specific transport characteristics.

As a final point in our analysis, we focus on simulated ΔXCO2‾ values for these four target dates (Fig. ). The ΔXCO2‾ values (blue line) on 3, 4, 6 and 10 July in five sampling sites are mainly dominated by the XCO2 changes caused by the anthropogenic tracer (red) instead of the VPRM tracer (green). Compared to Fig. a–d, the red line and blue line in Fig.  show a stronger similarity in their trends. With this form of DCM (compared to the original form Eq. 5 in Sect. 4.1), anthropogenic activities can be clearly shown to influence XCO2 within urban areas. Meanwhile, the ΔXCO2‾ measurements (black lines) fit better with the simulation with an RMSE of 0.2333 ppm compared to the comparisons of ΔXCO2 depicted in Fig. a–d (RMSE of 0.2973 ppm).