The core component of AUMIA v1.0 is the Weather Research and Forecasting (WRF) model (Skamarock et al., 2021). WRF is a fully compressible, non-hydrostatic model supported by the National Center for Atmospheric Research (NCAR) for a worldwide community of users. Due to its robustness and versatility, WRF has been widely used for operational forecasts and research related to severe weather and air pollution (e.g. Vara-Vela et al., 2021), the latter through the use of its chemistry extension, the WRF-Chem model (Grell et al., 2005). The WRF Greenhouse Gas model (Beck et al., 2011), hereafter referred to as WRF-GHG, is selected as the forward modelling component of AUMIA. WRF-GHG is an extension of the WRF-VPRM model (Ahmadov et al., 2007), which couples the WRF model to the Vegetation Photosynthesis and Respiration Model (VPRM) (Mahadevan et al., 2008).

WRF-GHG simulates CH4 concentration based on emission estimates from external data sets as well as from online calculations driven by model parameters such as soil moisture, soil temperature, and vegetation type. CH4 fluxes from external data sets, specifically for anthropogenic (except for biomass burning) and biomass burning sources, are converted into atmospheric concentrations based on an incremental approach. The CH4 concentration changes are calculated as the CH4 emission multiplied by a conversion factor that depends on the air density and thickness of the first model layer. On the other hand, CH4 fluxes from wetlands and termites, as well as CH4 uptake by soil, are all calculated online in the simulations (see Sect. 2.2.2 for further details). CH4 contributions from anthropogenic, biogenic (wetlands, termites, and soil uptake), and biomass burning sources as well as those from background concentrations are separately determined using tagged tracers. WRF-GHG allows for passive transport (i.e. without any chemical loss or production) of not only CH4 but also of carbon dioxide and carbon monoxide, which undergo advection and convective mixing as any other chemical species. WRF-GHG was incorporated into the WRF-Chem model for the first time at its version 3.4 and since then has been one of the many available chemistry options in this model. A detailed description of the WRF-GHG model, its emission preprocessors, and related modules can be found in Beck et al. (2011) and Beck (2012). In this work, WRF-GHG was run as a chemistry option in the WRF-Chem model version 4.3. Implementing the AUMIA v1.0 will enable us to extend its application to other greenhouse gases such as carbon dioxide, e.g. by incorporating new satellite missions such as the Copernicus Anthropogenic Carbon Dioxide Monitoring (CO2M).

Initially, a model sensitivity analysis for evaluating physics schemes, such as planetary boundary layer and cumulus clouds and global forcings for meteorological fields and CH4 concentration, was carried out over several 2-week periods in 2018 and 2019. Each of these 2-week periods were previously examined to have at least 75 % of days with TROPOMI XCH4 data covering large portions of Europe. As a result, the physics schemes Yonsei University (YSU) for the planetary boundary layer and Kain–Fritsch for cumulus clouds, together with initial and boundary conditions from the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) model (Hersbach et al., 2022) for meteorological processes and from the NCAR Community Atmosphere Model with Chemistry (CAM-chem) (Lamarque et al., 2012; Emmons et al., 2020) for background concentrations of CH4, were selected and then used to perform a 1-year simulation period from 1 April 2018 to 31 March 2019. This period was defined based on the following criteria: (i) availability of TROPOMI XCH4 data, (ii) latest available year data of EDGARv6.0 emissions for CH4, and (iii) no occurrence of sustained and irregular scenarios in terms of emissions (e.g. large-scale fire outbreaks and emission reductions associated with COVID-19 lockdowns). Table 2 lists the physics and emissions schemes used in the simulations, with physics schemes other than planetary boundary layer and cumulus clouds being selected based on Beck et al. (2011). A schematic of the model running process is depicted in Appendix A. Off-line initial and boundary conditions derived from the simulations at 30 km are used as input to feed the simulations at 10 km. Model results and discussion for the nested domain are under development and will be described in a forthcoming paper.

There are a number of statistical parameters that can be used to evaluate the performance of atmospheric models, including the correlation coefficient (r), mean bias error (MBE), and root-mean-square error (RMSE). r is a measure of the strength and direction of the linear relationship between simulation and observation, MBE measures the mean difference between simulation and observation, and RMSE is the square root of the mean squared error between simulation and observation. All three are appropriate over multiple timescales and space scales and can be calculated as follows: 4r=∑Pj-P¯xOj-O¯]∑Pj-P¯2x∑Oj-O¯2,5MBE=1n∑Pj-Oj,6RMSE=1n∑Pj-Oj2. Here, j represents the pairing of observations (O) and predictions (P) by site and time. Overbars signify means over site and/or time. n is the number of pairs of observation–prediction values.

In conjunction with the statistics previously mentioned, graphical methods such as time series, scatter plots, and Taylor diagrams (Taylor, 2001) were also included to better understand the model behaviour over entire ranges of concentrations and gauge performance more fully. To facilitate the statistical evaluation of the model–satellite comparison, both the satellite and model data were transformed into one-dimensional arrays. Subsequently, Eqs. (4), (5), and (6) were applied to compute domain-wide statistics. Overall, as described in Sect. 3, the simulated CH4 concentrations were in good agreement with the satellite information and near-surface measurements reported at different ICOS sites across Europe. However, several limitations and uncertainties were identified and will help to improve the model's forecast capability in future implementations.

Given that the distances between the model grid points and ICOS sites can be several kilometres, it is important to highlight that the model evaluation in this section focuses more on the model's ability to reproduce the broad spatial and temporal variability in CH4 over the modelling domain. As mentioned in Sect. 2.2.2, three sets of eight, six, and five ICOS stations, with sampling heights between 8.0–16.8, 40–50, and 100 m, respectively, were selected for comparison with simulated CH4 concentrations interpolated to roughly 10, 50, and 100 m above ground level. Figures 3, 4, and 5 show the monthly mean spatial distributions of observed and simulated CH4 concentrations for the first, second, and third vertical levels, respectively, with both data sets averaged over the period from 1 April 2018 to 31 March 2019. Figure S2 in the Supplement shows the monthly mean time series of CH4 concentrations averaged over all ICOS stations and corresponding model grid points for the three levels.

Overall, CH4 concentrations for the first level were overestimated, mainly during wintertime when model–observation mismatches reached their highest values, between 200 and 300 ppb (see Fig. S2 in the Supplement). According to modelling results in this study, the simulated CH4 concentrations depended largely on the background concentrations, followed by a small contribution from anthropogenic sources. A small month-to-month variation is observed in the CH4 concentrations from ICOS measurements, whereas strong seasonal changes are, by contrast, observed in the CH4 concentrations derived from model simulations – seasonal changes in the simulated concentrations are modulated by the anthropogenic sources. Using EDGARv6.0 CH4 fluxes as the a priori emission estimates and two sets of TROPOMI-based XCH4 observations, the global inversion approach conducted by Tsuruta et al. (2023) showed that over central Europe the anthropogenic CH4 emissions would be slightly overestimated, mainly during spring and autumn. However, higher emission estimates are otherwise found when ground-based data are used to drive the inversions. The inversion approach for CH4 emissions over China conducted by Hu et al. (2023) showed that the a posteriori emissions (excluding agricultural soil) decreased by 36 % compared to the EDGARv6.0 a priori emission estimates. They also found a 47.1 % reduction when it came to CH4 emissions from waste alone. Waste emissions in EDGARv6.0 for 2018 do not have a significant daily and weekly patterns over the year, although emission peaks can be observed in February. Under real conditions, however, the production of CH4 from waste sources depends not only on the amount of degradable organic matter but also on seasonal weather conditions (Kissas et al., 2022). Uncertainties in EDGAR emissions from other key sectors such as agriculture and energy can also contribute significantly to the overall model–observation discrepancies. For the EU27+UK (the 27 European countries and the UK), Solazzo et al. (2021) reported that while CH4 has the best level of accuracy among the three EDGAR greenhouse gases, with only a roughly 10 % uncertainty share, the structural uncertainties in the three key sectors in terms of CH4 (agriculture, waste, and energy) account for nearly 90 %.

Comparatively, model–observation discrepancies in CH4 concentration at upper levels (50 and 100 m) were noticeably reduced with increasing height (see Fig. S2 in the Supplement). The bias reductions in this case are attributed to a diminishing influence of surface emissions on both magnitude and variability in CH4 concentrations. The top-left panel in Fig. S4 in the Supplement shows the reductions in variability as a function of standard deviation, based on a site-specific comparison. The higher the sampling height (or vertical level), the smaller the model–observation discrepancies in terms of standard deviations are. Despite improvements in terms of variability, correlation coefficients remained quite similar between the three levels, ranging from 0.2 to 0.4 in most cases. Model evaluation of the global CAMS chemical modelling system against ICOS measurements, for the sites here selected and for a period 2.5 years from now (https://global-evaluation.atmosphere.copernicus.eu/ch4/ghg/insitu-icos, last access: 8 November 2022), shows structural correlation coefficients similar to those found here with WRF-GHG. However, unlike the large positive bias found in this work for the sampling height of 10 m, CAMS does underpredict the observations with model–observation discrepancies ranging from -100 to -200 ppb most of the time. In addition, no bias reduction with increasing height can be noticed in this CH4 product. Input emissions from anthropogenic sources in CAMS simulations are built based on various existing data sets, including nationally reported emissions as well as global estimates (e.g. EDGAR; Evaluating the Climate and Air Quality Impacts of Short-Lived Pollutants, ECLIPSE; and CEDS, Community Emissions Data System). As pointed out by Solazzo et al. (2021), the fact that EDGAR has adopted the IPCC recommendations assures consistency in time and comparability across countries, but conversely, it can facilitate the propagation of uncertainties when similar emission sources are incorporated.

Besides errors in the CH4 emission estimates, inaccuracies in background concentrations and meteorological conditions may have also partly contributed to model–observation discrepancies. With regard to the contribution from background concentrations, boundary conditions in the lowest model layer in CAM-chem are set to the fields specified for Climate Model Intercomparison Project – Phase 6 (CMIP6) historical conditions and future scenarios provided by Meinshausen et al. (2017). These prescribed CH4 concentrations are then used in the model to overwrite, at each time step, the corresponding model mixing ratios (Lamarque et al., 2012). Thus, the combined effect of using uniform and projected CH4 concentrations as lower boundary conditions in WRF-GHG simulations represents a source of uncertainty and contributes to the model–observation discrepancies. Regarding the meteorological conditions, unprecedented warmer than normal weather conditions were observed throughout the study period (Hari et al., 2020), mainly during the 2018–2019 winter season. In fact, model simulations for the period from 21 December 2018 to 14 January 2019 were not included in the model evaluation due to persistent instabilities in vertical winds over central Europe, where a sequence of heavy snowfall events has been observed (e.g. Yessimbet et al., 2022). As can be seen in Fig. S3 in the Supplement, the model overpredicted the temperature at 10 m throughout the entire winter, with overpredictions for December (averaged over 1–20 December 2018) and January (averaged over 15–31 January 2019) being much larger compared to the other winter months. Wind shifts were fairly well represented by the model, but at the same time, it did overpredict wind speed. A site-specific model evaluation in terms of correlation coefficient and standard deviation is provided in Fig. S4 in the Supplement.

Figure 6 shows the temporal mean spatial distributions of XCH4 concentration from SRON RemoTeC-S5P estimates and WRF-GHG simulations, along with their relative differences, averaged over the period from 1 May to 31 August 2018. Temporal mean spatial distributions by month are shown in Figs. S5 to S16 in the Supplement. Differences between simulated XCH4 concentrations with and without smoothing are noticeable. While relative differences between simulated concentrations without smoothing and observational data usually range from -1 % to 1 % (Fig. 6g), those between smoothed concentrations and observational data usually range from 1 % to 2 % (Fig. 6c). Model–observation discrepancies in the latter case reached their minimum values during the summer peak season (Figs. S7 to S9 in the Supplement) but otherwise reached their maximum values during winter months (Figs. S14 to S16 in the Supplement). Model performance for different seasons can be also observed in Fig. 7 which shows the monthly variability in observed and simulated XCH4 concentrations over the study region. The lower differences between the satellite measurements and model results without smoothing were related to a CH4 offset (against the anthropogenic emissions contribution), as the atmospheric layer above the model top (1 hPa) was not vertically integrated in Eq. (3). Simulated CH4 concentrations and atmospheric pressures in this case did not experience any smoothing before vertical integration. Regarding the smoothed profiles, despite the fact that it was verified that the averaging kernels from satellite retrievals fluctuate slightly up and down around 1 in the troposphere (where much of atmospheric CH4 resides), the smoothing effects in the upper levels usually lead to a XCH4 reduction. This reduction often happens because the a priori profile (second term on the right-hand side of Eq. 1) does not influence the retrieval accuracy significantly (Hu et al., 2016). Since there is no CH4 compensation in this case, then the bigger differences in the XCH4 concentrations can be attributed mainly to an overestimation of anthropogenic emissions, although a systematic bias related to background signals should also be considered. At an urban scale, analysis of downwind and upwind concentrations such as the differential column methodology devised by Chen et al. (2016) can be applied to minimize the influence of background signals (e.g. Zhao et al., 2022); however, its application at a continental scale would require a high-resolution modelling configuration as well as a dense network of spectrometers. Data gaps such as those observed in central and southern Europe (Fig. 6a or e) are often produced as a consequence of applying regridding techniques to sparse data sets.

Zhao et al. (2019) applied the WRF-GHG model to analyse XCH4 observations over Berlin for a period during summertime and found a bias in the simulated XCH4 concentration of around 2.7 %. In this case, they updated the boundary conditions with information from CAMS instead of CAM-chem, used EDGARv4.1 emission estimates for anthropogenic sources, and compared the model results against total-column measurements from a network of five spectrometers. Based on the smoothed concentrations in this work, relative differences between 1 % and 2 % were often found for the summer peak season, when the anthropogenic sources had their minimum contributions to the XCH4 concentration. For winter months, the differences were found to range from 2 % to 3 %, similar to those found by Zhao et al. (2019) for summertime. Despite the fact that a model overestimation of near-surface CH4 concentrations on the order of 200–300 ppb is observed during wintertime, the model–observation discrepancies in XCH4 concentration ranged roughly from 40 to 60 ppb. The higher model–observation discrepancies during winter months suggest that a more refined inverse analysis assessment will be required for this season. A recent joint inversion of CH4 and δ13C-CH4 conducted by Basu et al. (2022) for periods of relatively stability (2000–2006) and growth (2008–2014) in atmospheric CH4 suggests a significant reduction in the a priori CH4 emission estimates from fossil and microbial sources over northern extra-tropic regions. Bias in simulated XCH4 concentrations over waterbodies, namely the Mediterranean Sea, the Bay of Biscay, and small portions of the Atlantic Ocean adjacent to Spain and Portugal, is of similar magnitude as that found over land. Thanks to the TROPOMI's wide swath, the SRON S5P-RemoTeC XCH4 product v17 provides new opportunities to look into the sensitivity of CH4 signals to surface emissions in the Mediterranean Sea (e.g. CH4 emissions from oil and gas platforms).

With regard to temporal variability, a clear annual cycle of the XCH4 interquartile range can be noticed regardless of its smooth month-to-month variation throughout the year (orange boxes in Fig. 7). Both sets of simulated XCH4 concentrations, i.e. the simulated profiles with and without smoothing, represented this cycle fairly well although with less dispersion (length of the box). The simulated XCH4 concentrations without smoothing show an even less dispersed interquartile range (blue boxes in Fig. 7) compared to that of the smoothed concentrations (green boxes in Fig. 7). In addition, the minimum concentrations in the simulated interquartile ranges are delayed (May) compared to observations (April), with the same happening in terms of medians. Based on the smoothed concentrations, model–observation discrepancies reached their maximum values during winter months (differences in median concentrations between 40–50 ppb), while they reached their minimum values during the summer peak season (differences in median concentrations between 20–30 ppb). As discussed in Sect. 3.2, the improved XCH4 representation (with the simulated profiles without smoothing) responded to a CH4 compensation, as the atmospheric layer above the model top (1 hPa) was not vertically integrated in Eq. (3). Since there is no a CH4 compensation with the smoothed profiles, then the bigger differences in the XCH4 concentrations can be attributed mainly to an overestimation of anthropogenic emissions. A systematic bias related to the background concentrations, however, should be also embedded in the model bias in both cases. Modelling studies using CAMS suggest that an offset between model concentrations and observations needs to be taken into account previously in the boundary conditions (Zhao et al., 2019; Gałkowsky et al., 2021). Looking at the other 50 % of data, including outliers, a similar behaviour can also be observed, with observations spread out further than simulated concentrations. A number of outliers with concentrations below 1750 ppb have been observed in April and May of 2018, although the reason why they occur in the months with the lowest CH4 concentrations needs to be further investigated. Statistical metrics of the model–observation comparison indicate, overall, a better model performance for summer months, with correlation coefficients and root-mean-square errors ranging from 0.4–0.5 and from 27–30 ppb, respectively (see Table 4).