The Icosahedral Nonhydrostatic (ICON) weather and climate model is a collaborative effort between the Deutscher Wetterdienst (DWD), the Max Planck Institute for Meteorology (MPI-M), the Deutsches Klimarechenzentrum (DKRZ), the Karlsruhe Institute of Technology (KIT), and the Center for Climate Systems Modeling (C2SM) in Switzerland. Its goal is to develop a unified, next-generation global system for numerical weather prediction (NWP) and climate modeling. ICON became operational within DWD's and MeteoSwiss' forecasting systems in 2015 and 2024, respectively. Notably, ICON was made available as open-source software to expand its user and developer community in February 2024. To incorporate atmospheric chemistry and aerosol processes, ICON is extended by the Aerosols and Reactive Trace gases (ART) module, developed and maintained by KIT . This combination forms the ICON-ART model, a non-hydrostatic Eulerian chemical transport model that includes emissions, transport, gas-phase chemistry, and aerosol dynamics in both the troposphere and stratosphere. ICON-ART uses an icosahedral grid that can cover the entire globe or be restricted to limited areas, ranging in horizontal resolution from several degrees down to a few kilometers.

For the present study, the model is configured with a horizontal resolution of 26 km (approximately 0.3°) over Italy and its surroundings (2–24° N, 32–54° E), consisting of 5048 grid cells (see Fig. , upper panels). Vertically, the model extends from the surface up to 23 km with 60 levels, using a height-based, terrain-following coordinate system.

Meteorological variables are computed online by the ICON model. In this setup, key prognostic variables (including wind speed, specific humidity, density, virtual potential temperature, and Exner pressure), are weakly nudged toward ERA5 reanalysis data from the ECMWF, available at a 3-hourly temporal resolution. This nudging helps maintain the model's realism and prevents significant drift from observed atmospheric conditions. ERA5 data also provide the model's initial state. We simulate the year 2018 to be consistent with .

Emission fields for transported species are processed via the Online Emissions Module OEM;, integrated within ART. Output files of instantaneous concentrations are saved hourly and later interpolated in time, height, and space to derive model equivalents of observational data.

We do not consider atmospheric sinks as the air (along with emissions) is flushed out from our European domain in less than 20 d. We therefore neglect the effects of CH₄ oxidation in the atmosphere, as typically done in European inversions.

The Community Inversion Framework CIF; is an inversion system that has been designed to bring together the different inversion methods (analytical, variational and ensemble) and transport models used in the inversion community. It is built as an open-source, well documented, highly modular multi-model inversion framework written in Python that facilitates the comparison of (1) inversion methods and (2) transport models. CIF has proved to be accurate and computationally performant over the past years

We employ the ensemble square root filter (EnSRF) algorithm implemented in CIF to perform the inversions presented in this study. This algorithm has recently been improved and is thoroughly described in . Briefly, an ensemble of vectors is used to represent the probability distribution of the control vector, which contains all the variables that we wish to optimize (e.g., fluxes, background concentrations, etc). Each member of the ensemble is attached to a different tracer transported by the model. After running simulations with this ensemble of tracers, the resulting ensemble of output concentrations is used to optimize the control vector to minimize the mismatch with the assimilated observations of atmospheric concentrations. In this study, the variables being optimized are scaling factors applied to the fluxes at the model's horizontal resolution.

The full assimilation time period is partitioned into several windows of finite length. For each window, a single scaling factor is associated with each optimized variable (e.g., flux emitted in a cell of the horizontal domain). Scaling factors within the window are optimized using both the observations from the current window and the observations from a fixed number (lag) of subsequent windows. Covariance localization is also applied to mitigate spurious long-range correlations that tend to appear in the ensemble. More details about the exact setup employed for this study is provided in Sect. .

The prior information is based on several high-quality datasets, which are merged into two categories of emissions: anthropogenic and natural. Total, anthropogenic and natural emissions are shown in Fig.  (upper panels).

For selecting candidate stations for the extended ICOS network, we consider 8 locations from Italy's existing or planned monitoring infrastructure:

Mount Venda (VND, 45.3° N, 11.7° E). It is a proposed new site intended to improve constraints on emissions in the high-emission Po Valley region. A preliminary study investigated the possibility of installing a GHG sampling inlet at a transmission tower on the summit of Mount Venda (570 m), in the eastern Po Valley. However, this remains at the planning stage due to funding limitations.

ECO, LMT, CGR, CUR, MDN, and MRG are not part of ICOS but contribute to the regional Global Atmospheric Watch (GAW) programme of the WMO, which motivated their selection as candidate sites. Further information about these stations is provided in Table . Locations are displayed on a spatial map in Fig.  (e.g., Scenario 11). For stations already measuring CH₄, the ICOS label would require compliance with ICOS standards for measurement systems, quality-assurance protocols, as well as the adoption of a common data format for the near-real-time transmission of instrumental and diagnostic raw data to the ICOS Atmospheric Thematic Center . Moreover, a sustained long-term commitment from national funding agencies is required to support the operational costs of the stations, as well as the national contributions required to ensure the operation of ICOS-labelled stations and their integration within the ICOS Research Infrastructure.

This study evaluates twelve atmospheric measurement network scenarios encompassing Italy and its neighboring countries. The primary goal is to determine which candidate stations, introduced in Sect. , would provide the greatest benefit for constraining emissions in Italy. It results in eight different scenarios, each featuring one of the candidate stations. In addition, several supplementary network scenarios are considered to assess the contribution of existing networks and to estimate the optimal achievable constraints on Italian emissions. The twelve scenarios, displayed in Fig. , are outlined as follows:

Scenario 1 includes only ICOS sites located in countries neighboring Italy. This configuration serves to assess the ability of external networks to constrain emissions originating within Italy.

These scenarios enable a systematic evaluation of how different network configurations influence the capacity to monitor and constrain GHG emissions across the region.

Synthetic observations generated with the transport model ICON-ART are assimilated by the inversion system to refine prior estimates and to assess the potential of each candidate station for constraining emissions. Conducting robust OSSEs to identify the most suitable stations for network expansion requires producing synthetic observations with times and locations that closely replicate those of real-world measurements.

For existing stations, we use synthetic observations matching the locations and times of the real observations compiled in version 9.2 of the ICOS ObsPack CH₄ data product . This dataset includes continuous measurements from 66 stations across Europe collected between 1984 and 2024, encompassing both ICOS and non-ICOS facilities. Within the temporal and spatial bounds of our experiments, data from 19 stations are available (blue and yellow circles in Fig. ), with detailed station information provided in Table .

For both candidate and ecosystem stations, hourly measurements are assumed. To replicate the methodology of an inversion assimilating real data, only a subset of synthetic observations is used. At lowland sites, only the daily average of afternoon observations between 12:00 and 16:00 LT (local time) is assimilated to avoid challenges associated with simulating the boundary layer growth over the day. In contrast, at mountain sites, only the daily average of nighttime observations between 00:00 and 06:00 LT is assimilated, when these stations are more representative of background conditions and are less influenced by pollution transported by daytime upslope valley winds.

Regarding the required infrastructure, the main constraint was to remain consistent with the inlet heights assumed in . In that study, a low inlet height of 2 m is used for mountain candidate sites, whereas a higher inlet height of 100 m is used for lowland candidate sites. Note that CHI is an exception, both here and in , as it is a newly established station. At the start of this study, the projected inlet height was 50 m. We retained this value in our analysis because the installation of a substantially higher inlet in the coming years is considered unlikely.

The rationale behind the selection of 2 m and 100 m inlet heights is that model performance generally improves with increasing sampling altitude, provided that the surrounding terrain is not excessively complex and does not generate strong local flow disturbances. Higher sampling altitudes reduce the influence of very local processes, which require high spatial resolution to be accurately represented. Elevated sampling also increases the spatial footprint of the measurements, allowing observations to integrate signals from more distant source regions and thereby increasing sensitivity to large-scale flux patterns. However, sampling at excessively high altitudes, such as mountain stations located above the boundary layer, also has disadvantages. Air masses sampled at these altitudes are well mixed, making it more difficult to disentangle contributions from individual source regions. Consequently, such measurements are generally more effective at constraining background concentrations than regional emissions.

For lowland sites, a good sampling at existing ICOS sites is typically performed at around 100 m above ground level (see Table ). This height helps reduce the influence of local processes, and obtain a good sensitivity to regional fluxes, while limiting costs and engineering challenges. At present, however, candidate stations that have previously measured CH₄ (ECO, LMT, CGR) sample below 100 m. Reaching such sampling heights would therefore require the installation of tall towers. Although this represents a substantial investment, implementation is expected to be more feasible at these locations because they already possess relevant infrastructure and experienced personnel conducting CH₄ measurements

For mountain sites, nighttime measurements are generally representative of the free troposphere, even when sampled close to the surface, owing to the elevated location of the stations. As a result, a sampling height of 2 m is sufficient, and this requirement is already met by existing mountain stations performing CH₄ measurements (MDN and CUR).

To generate synthetic observations with the ICON-ART transport model, we first sample a set of “true” scaling factors (representing the ratio of true to prior emissions) for each grid cell in the ICON-ART domain (c=5048 cells), following the approach described by . We briefly present this approach here.

The true scaling factors are sampled from a normal distribution with a prior-error covariance matrix B. We account for both spatial and temporal correlations. For spatial correlations, we first construct a correlation matrix based on an exponential decay function, e-di,jL, where di,j denotes the great-circle distance between cells i and j, and L is the spatial correlation length. We then scale this matrix by the chosen variance to obtain the spatial covariance matrix. A similar procedure is applied to introduce temporal correlations, replacing spatial distances with the time interval between similar optimized variables (i.e., corresponding to the same cell), normalized by the temporal correlation length. The full covariance matrix, accounting for both spatial and temporal correlations, is built using Kronecker products. Using the singular value decomposition (SVD) of the full matrix B, we generate an ensemble of spatially and temporally correlated scaling factors. A major advantage of this approach is that it generates true fluxes consistent with the error statistics of the prior fluxes.

Distinct sets of true scaling factors are generated for anthropogenic and natural emission categories, and true total fluxes are computed as the sum of the true anthropogenic and natural fluxes. In line with the recommendations of and anthropogenic correlation lengths estimated by TNO for Italy , we adopt a spatial correlation length of 200 km for natural fluxes and 100 km for anthropogenic fluxes, considering no correlation for fossil fuel emissions and a correlation length of 150 km for agriculture and waste emissions. To determine the appropriate variance for each scaling factor, we compute the country-scale uncertainty for both flux categories using the specified correlation lengths and a range of relative variances (50 %, 100 %, 150 %, 200 %). Our analysis suggests that relative variances of approximately 150 % are required for both natural and anthropogenic fluxes to match the country-scale uncertainties reported by TNO (for anthropogenic fluxes) and by (for both flux categories in Italy). However, applying relative variances above 100 % within a Gaussian framework increases the risk of generating negative flux values during the inversion. To balance realistic uncertainty representation with these technical constraints, we adopt a relative variance of 100 % for both flux categories. Although it results in a prior uncertainty that is slightly underestimated compared to existing estimates, it should not affect the conclusions of this study as we use an inversion set-up where true uncertainties are considered to be perfectly known. Note that, due to the shorter correlation length applied to anthropogenic fluxes, it results in a lower country-scale uncertainty for anthropogenic emissions compared to natural ones.

To account for a potential temporal variability of the mismatch between prior and true estimates, we generate a new set of true scaling factors for each 10 d period throughout the year 2018. To maintain seasonal coherence, we impose a temporal correlation using an exponential decay with a temporal correlation length of three months. An example of the resulting scaling factors, averaged over 2018, are shown in Fig. a. The perturbed fluxes used as the synthetic “truth” are obtained by applying these scaling factors to the corresponding prior fluxes. The selected values for prior relative variances and for spatial and temporal correlations lengths are summarized in Table .

Finally, we run a 1-year forward simulation over 2018 with the perturbed fluxes. After this forward simulation, the simulated values matching the time and locations of the observations (for existing stations) or pseudo-observations (for candidate and ecosystem stations) introduced in Sect.  are stored. These simulated values are then treated as the new observations to be assimilated in the experiments presented in the next section. Additionally, to mimic realistic model-data mismatch uncertainties arising from both modelling and measurement errors, we perturb them with random values drawn from a Gaussian distribution with a mean of 0 and a standard deviation of 20 ppbv. This corresponds to the typical model-data mismatch calculated in with ICON-ART runs at a resolution of 26 km.

To cover a wider range of emission uncertainties, we replicate this methodology five times to generate five different sets of synthetic observations based on five different sets of true fluxes (hereinafter called truth scenario). The importance of using different truths for an OSSE is illustrated and discussed in Sect. .

Model–data mismatch plays a critical role in atmospheric inversions, as it directly affects the assimilation weights assigned to each observation and, consequently, the inversion outcomes. Assigning a uniform model–data mismatch across all stations implies equal trust in all observations. However, in real-data applications, model–data mismatch is inherently site-dependent. It reflects the degree of confidence in the model's ability to accurately simulate concentrations at a given location, which can vary due the model's ability to capture local atmospheric dynamics and local sources, given the complexity of the surrounding environment. In Sect. , we present a refined, station-specific estimation of model–data mismatch and analyze its impact on the inversion results. We chose to introduce results with a uniform model-data mismatch first, before incorporating the additional complexity associated with a realistic model-data mismatch. This choice serves several purposes in the initial phase of our study. First, it provides a consistent and fair basis for comparing candidate stations, which would not be possible with a realistic model-data mismatch that varies across locations. Second, there is no guarantee that the model-data mismatch estimated using our methodology will accurately reflect real conditions once a station becomes operational. In practice, experience shows that trying to predict how well a model will reproduce observations from a new station is highly challenging. Finally, it facilitates the interpretation of the results. Using a uniform model-data mismatch is not sufficient on its own, which is why we present results from both approaches.

For each designed network and each set of true fluxes and perturbed observations, we run a 1-year inversion (i.e. 12 network scenarios × 5 truth scenarios = 60 inversions) spanning 2018 with the EnSRF mode of CIF-ICON-ART. Following the conclusions of , we use the following CIF settings to run all the inversions:

Window length = 10 d

To build the prior error-covariance matrix B, relative variances and spatial and temporal correlations are prescribed to match the values used in generating the true scaling factors (see Table ).

We use two different metrics to quantitatively compare network designs: error reduction and uncertainty reduction. Here, we define these metrics.

Figure  shows the MER for total CH₄ emissions across four regions (all of Italy, Northern Italy, Central Italy, and Southern Italy) for each network scenario, and averaged over the five truth scenarios. In Scenario 1, which includes only neighboring stations, Northern Italy exhibits a moderate constraint with MER, reaching 18.0 %. In contrast, the capacity of the network is slightly weaker in Central Italy (MER < 15 %), while Southern Italy remains essentially unconstrained, with MER as low as 3.9 %.

Including the existing ICOS stations within Italy (Fig. , Scenario 2) markedly improves the agreement between posterior and true fluxes, raising MER by about 5 %–10 % across all regions. However, Southern Italy remains poorly constrained by the existing ICOS network compared to the other regions.

Analysis of individual candidate stations indicates that Mount Venda (VND) and Chieti (CHI) perform best, each achieving 1 %–2 % higher MER than other sites (Fig. , Scenarios 3 and 4). VND is particularly effective in Northern Italy, whereas CHI provides stronger constraints in Central and Southern Italy, outperforming all the other candidate stations in those regions. Other stations, such as Lecce (ECO) and Capo Granitola (CGR), also improve network performance reasonably. While ECO captures information about emissions both in Central and Southern Italy, CGR improves the coverage in Southern Italy.

Idealized expansion (i.e., adding all candidate stations in Scenario 11 and the full set of ICOS ecosystem stations in Scenario 12) provides substantial gains, with MER for all of Italy reaching 27.6 % and 38.5 %, respectively. While Northern and Central Italy shows similar results under Scenario 12, Southern Italy remains less constrained. This comparatively weak constraint can be attributed to three factors:

Small flux signals: Enhancements observed at Southern stations are comparable to or lower than the model–data mismatch, limiting the inversion's ability to attribute them to specific sources. By contrast, larger enhancements at VND and CHI allow for clearer source identification.

The TUR results (see Fig. ) are consistent with these findings. CHI and VND yield identical, and the largest, uncertainty reductions, exceeding those of other sites by approximately 4 %. VND has the strongest influence in Northern Italy, whereas CHI provides greater benefits in the rest of the country.

These results underscore the importance of the CHI and VND sites for constraining CH₄ emissions in Italy, identifying them as the strongest candidates for extending the ICOS network in the country. Behind CHI and VND, ECO and CGR are also good candidates.

Figure  shows MER for all truths, emphasizing the large variability of results one can infer using different truth scenarios. At the national scale, the MER is found to vary by up to 5 % around the mean (Fig. a, gray range), which is large compared to the differences between scenario results. The truth has such an importance because the posterior scaling factors typically remain unchanged compared to the prior (i.e., close to 1) over areas where there are no monitoring stations because of a lack of information. If the true scaling factors are also close to 1 over these areas, the agreement will appear to be large not because of constraints provided by the network, but because of randomness. For example, in second truth scenario, some grid cells have true scaling factors already close to 1 in Central Italy (Fig. S3, panel 2a). The posterior values also stay close to 1 because of a lack of observations, and the artificial agreement between the truth and posterior estimates leads to a good MER. By contrast, MER in the fourth truth scenario (Fig. c, purple rectangle) is notably low in Central Italy compared to the other truth scenarios, for most of the candidate stations. This arises because the fourth scenario includes a patch of high (randomly generated) scaling factors over this region in the true natural emissions, close to a patch of low values in Northern Italy (Fig. S3, panel 3b). Due to the lack of observational constraints, the system cannot properly disentangle these values, and the posterior scaling factors remain close to 1 on a large portion of Central Italy, leading to a small MER. These results highlight that a robust assessment can only be achieved by using an ensemble of truth scenarios that captures the spread of emission uncertainties.

On the contrary, results for TUR are not dependent on truth scenarios. This is because the posterior error covariance matrix in Eq. () is a function only of the error covariance matrices (i.e., the prescribed prior relative uncertainties, correlation lengths, and model-data mismatch) and the transport model (see and references therein).

Because different truth realizations can yield different MER outcomes, it is important to assess how often one station provides stronger constraints than another, i.e., the probability that adding one station improves MER more than adding a different station. Figure  presents these pairwise comparisons. At the national scale, adding CHI outperforms VND in terms of MER for 80 % of the truth realizations (Fig. a, first line). This highlights the importance of using different truth scenarios. Using only one scenario could have resulted in preferring VND over CHI. In Northern Italy, VND consistently provides stronger constraints than CHI (100 % of the realizations) as well as any other station. In Central Italy, CHI almost always outperforms VND, while VND tends to be better than the remaining stations. In Southern Italy, CHI is consistently superior to both VND and the other stations. However, while averages over the truth scenarios suggest that ECO, Lamezia Terme (LMT), and CGR generally outperform VND in the South, a notable fraction of the realizations (20 %–40 %) indicate better performance for VND (Fig. d, three last lines). This highlights that, in some cases, VND can also provide stronger constraints than the Southern stations in Southern Italy.

These results confirm that CHI and VND would be the best choices to extend the ICOS network in Italy. In addition, it shows slightly stronger results in favor of CHI, although the difference is small.

Figures  and present MER (averaged across all network scenarios) and TUR for total, anthropogenic, and natural emissions.

At the national scale, MER and TUR for anthropogenic emissions reach about 10 % and 15 %–20 %, respectively, across all candidate stations. These emissions are best constrained in Northern Italy, where they are most intense: adding VND (Scenario 3) increases MER to 15 % and TUR to nearly 20 %, representing the strongest performance in this region. In contrast, anthropogenic emissions remain poorly constrained in Central and Southern Italy, with both MER and TUR below 10 %. Compared to total emissions, the weaker performance for anthropogenic emissions arises from two main factors. First, separating natural and anthropogenic contributions in the observed signal is intrinsically difficult. Without additional constraints (e.g., isotopic information), the inversion relies only on spatial and temporal differences. When natural and anthropogenic emissions are co-located and occur simultaneously, the optimization process cannot effectively separate them, resulting in poor agreement between the posterior and true fluxes for each category. Second, anthropogenic emissions are assigned a shorter spatial correlation length in the prior error covariance (Sect. ), following recent literature. While more realistic, this choice increases the number of degrees of freedom and thus the complexity of the inverse problem. In other words, the true scaling factors for anthropogenic emissions vary more spatially than those for natural and total emissions. As a result, constraining the higher heterogeneity of anthropogenic scaling factors with the same number of observations is more challenging, leading to poorer performance.

Natural emissions are therefore better constrained than anthropogenic emissions. They are more spatially diffuse and characterized by a larger spatial correlation length, making the metrics less sensitive to favorable wind conditions (i.e., transport from source regions to stations). Their performance closely follows that of total emissions, with MER values typically about 4 % higher across most regions, except in Southern Italy where they are nearly identical.

Across all regions, the conclusions for anthropogenic and natural emissions remain consistent with those for total emissions. Although anthropogenic emissions are only weakly constrained, CHI and VND consistently outperform the other sites across all categories, with VND performing best in Northern Italy and CHI in the remaining regions. The separation between anthropogenic and natural emissions is discussed further in Sect. .

As explained in Sect. , different sets of true scaling factors were generated for successive 10 d windows for both natural and anthropogenic emissions to account for a potential temporal variability in the associated uncertainties. This introduces a “true” seasonality in anthropogenic, natural, and total emissions that differs from the prior. We assess the inversion's ability to recover this true seasonality by analyzing the seasonal behavior of MER and TUR. Results are shown in Figs.  and , respectively.

To limit the number of abbreviations in this section, DJF, MAM, JJA, and SON are hereinafter also referred to as winter, spring, summer, and autumn, respectively. Seasonality can have a substantial influence on MER mainly through three drivers:

Larger flux signal differences: The inversion system can more effectively attribute and locate underlying sources when (1) the station captures the emission signal and (2) the resulting signal difference between prior simulated values and assimilated pseudo-observations, caused by discrepancies between prior and true emissions, exceeds the model–data mismatch. For example, if the discrepancy between prior and true emissions peaks during winter and the signal can be adequately captured by the stations, a higher MER will be obtained during that season. However, when evaluating the performance averaged over multiple truth scenarios, this specific driver is neutralized. Because each scenario features a distinct random seasonal profile, averaging the performance eliminates the systematic influence of individual mismatches between prior and true emissions, thereby leaving only the influence of the other drivers introduced below.

For most network scenarios, the highest MER values for total emissions are achieved during summer or spring across all regions. Because Eulerian frameworks, unlike Lagrangian frameworks (see Sect. ), do not directly output footprint sensitivity maps, interpreting these results is inherently challenging due to the complex interplay between wind speed, wind direction, and vertical convection. Nevertheless, an interpretation can be proposed. The vigorous convective mixing characteristic of summer afternoons is likely a primary driver of the elevated MER values observed at both national and regional scales. Given our natural scaling factors exhibit large spatial correlation lengths, the enhanced constraint on emissions close to the stations in summer likely help to constrain broader regions sharing similar scaling factors. However, convective mixing alone cannot be the sole explanation. For instance, MER peaks during spring in Northern Italy but drops significantly during the same season in Central and Southern Italy, despite high convective mixing. In Northern Italy, this spring peak in 2018 was likely driven by stronger seasonal winds relative to summer. In contrast, for Central and Southern Italy, the lower spring MER is potentially tied to the specific meteorology of 2018, where strong, predominantly westerly winds limited the transport of inland emissions toward the monitoring sites. By summer, a shift to north-westerly winds allowed the stations to sample a greater fraction of inland emissions, thereby improving the constraint.

The TUR outcomes generally mirror those of MER, with one notable exception: autumn values align much closer to those of spring and summer than observed in the MER results. This relative improvement is likely driven by the highly variable wind directions across Southern and Central Italy during autumn 2018, which broadened the station footprints. While such wind variability does not necessarily improve MER, as it dilutes the peak emission signals and makes them less distinguishable, it might successfully reduce posterior uncertainty across a wider geographical area, thereby enhancing TUR.

Although seasonality affects both MER and TUR for individual network scenarios, the differences between scenarios show little seasonal variation; in other words, the seasonal influence is largely similar across all stations.

We evaluate the impact of incorporating a non-uniform model–data mismatch in our analysis. For real stations, this mismatch is estimated using observations from the AVENGERS obspack data product. For candidate stations, where observations are unavailable, we rely solely on simulated values.

For the real stations, we first perform a forward simulation for the year 2018. Simulated values are then sampled and compared to observations to compute an initial model–data mismatch using the root mean square error (RMSE). This initial estimate is used to perform an inversion for 2018. Following this initial inversion, we recalculate the RMSE using the posterior mole fractions, which provides a refined estimate of the model–data mismatch at these stations, and then perform a new inversion using this updated estimate of model-data mismatch. The results of this second inversion are analyzed.

For the candidate stations, a forward simulation for 2018 is conducted. In this case, we use the standard deviation of the simulated values at each station as a proxy for model–data mismatch. This approach was validated against real stations, showing a strong correlation with the RMSE-based estimates (r=0.96). We also tested alternative methods based on a moving average (7 d and monthly) of the simulated values, following , but found that it yielded weaker correlations. Such differences might be related to the fact that CO₂ concentrations often show strong hourly fluctuations driven by the diurnal cycle of photosynthesis and respiration, unlike CH₄. Therefore, a 7 d moving average may be suitable for CO₂ but less representative for CH₄.

Results obtained using the non-uniform model–data mismatch are provided in the Supplement. Most inferred mismatches exceed 20 ppb (Table S1), with a mean value of 31 ppb, indicating lower confidence in the measurements than initially expected. JFJ exhibits the smallest mismatch (14 ppb), whereas IPR and IT-BFt show the largest values (75 ppb). Large model–data mismatches suggest difficulties in capturing the observed variability at these stations. In particular, observations at IPR are known to be challenging for transport models due to the complex surrounding terrain. The CHI model–data mismatch (46 ppb) is estimated to be larger than that of VND (35 ppb), giving a slight advantage to VND compared to the experiments with a uniform mismatch. Using these new estimates of model-data mismatches, both MER (Table S2, Figs. S4 and S7) and TUR (Table S3, Figs. S5 and S8) decrease by 2 %–6 % compared to the experiments assuming a uniform model–data mismatch.

Nevertheless, the conclusions drawn in the previous sections remain unchanged: Scenarios 3 (VND) and 4 (CHI) continue to be the optimal choices for all of Italy when comparing MER and TUR values to other scenarios, with CHI retaining a marginal advantage.