Inverse modeling is a widely used top-down method to infer greenhouse gas (GHG) emissions and their spatial distribution based on atmospheric observations. The errors associated with inverse modeling have multiple sources, such as observations and a priori emission estimates, but they are often dominated by the transport model error. Here, we utilize the Lagrangian particle dispersion model (LPDM) FLEXPART (FLEXible PARTicle Dispersion Model), driven by the meteorological fields of the regional numerical weather prediction model COSMO. The main sources of errors in LPDMs are the turbulence diffusion parameterization and the meteorological fields. The latter are outputs of an Eulerian model. Recently, we introduced an improved parameterization scheme of the turbulence diffusion in FLEXPART, which significantly improves FLEXPART-COSMO simulations at 1 km resolution. We exploit F-gas measurements from two extended field campaigns on the Swiss Plateau (in Beromünster and Sottens), and we conduct both high-resolution (1 km) and low-resolution (7 km) FLEXPART transport simulations that are then used in a Bayesian analytical inversion to estimate spatial emission distributions. Our results for four F-gases (HFC-134a, HFC-125, HFC-32,

Monitoring greenhouse gas (GHG) emissions into the atmosphere is critical in order to determine whether they comply with our endeavor of limiting the average global temperature increase below 2

Atmospheric inverse modeling is a widely applied top-down emission estimation method

Errors in the inverse modeling estimates are introduced by errors in the atmospheric observations, in the estimate of the a priori, and in the error covariance matrices but are strongly driven by errors due to transport and representativeness inherent in the transport model

The inversions conducted in this study focus on some of the most important (by

In this study, we use the LPDM FLEXPART-COSMO

Newly available synthetic gas observations, collected as part of the Swiss National Science Foundation (SNSF) project IHALOME (Innovation in Halocarbon Measurements and Emission Validation), from the Swiss Plateau at the Beromünster and Sottens tall towers, complemented with observations from the Advanced Global Atmospheric Gases Experiment (AGAGE) network

The inversion system employed in this study is an analytical Bayesian inversion system

The paper is organized as follows: Sect.

The details of the observational sites used, such as their coordinates, their altitude, the air inlet height above ground, and the height of each site in the different transport model versions (Sect.

Details of the observational sites used in the study, including the location, altitude, and height of the model topography in the different FLEXPART model versions.

Measurement locations (black crosses) of sites used in the inversions as well as COSMO and IFS model domains (polygons) used as input to FLEXPART

The Beromünster (BRM) tall tower site (Table

Simulated total surface sensitivity (footprints) for Beromünster

The Sottens (SOT, Table

The Jungfraujoch (JFJ, Table

Two additional sites were used in the inversions conducted within this study: Mace Head (MHD) and Tacolneston (TAC), as shown in Table

Two more AGAGE sites were employed in sensitivity inversions to explore any further impact of additional observations on Swiss emissions: Monte Cimone (CMN) and Taunus Observatory (TOB), as shown in Table

In this study, we used observational data on 1,1,1,2-tetrafluoroethane (HFC-134a), 1,1,1,2,2-pentafluoroethane (HFC-125), difluoromethane (HFC-32), and sulfur hexafluoride (

The observational data employed for the inversions cover the period from August 2019 to October 2021. Data from TAC, MHD, and JFJ were used for the whole period, while BRM and SOT data were available only during the field campaigns. The campaign in BRM lasted from August 2019 to September 2020 and in SOT from March 2021 to October 2021. There was no temporal overlap because the same instrument had to be used at both locations. CMN and TOB observations were employed in sensitivity inversions for the BRM campaign period only. Measurements from TOB come from flask samples, which are collected weekly for offline analysis.

To run our inversions, 24-hourly (3-hourly for sensitivity inversion) mean values were produced from the available observations of the abovementioned sites. To correctly infer regional emissions from a limited model domain, accurate knowledge of the so-called background (or baseline) mole fraction of a compound is needed. An observed mole fraction of a compound can be decomposed into a baseline fraction,

An underestimation of the baseline will magnify an emission event, whereas an overestimation will reduce the intensity of an emission event. We estimate our baseline mole fractions by using the robust extraction of the baseline signal (REBS) method

Other statistical methods for baseline estimation have been applied to greenhouse gas observations

The inversion system utilized for this study is comprised of an atmospheric transport model, which relates the spatial emissions,

COSMO is a non-hydrostatic limited-area atmospheric model. It was initially designed for operational NWP by the German weather service (DWD), and it is still used by several national weather services including MeteoSwiss

High-resolution (HRES) IFS is the operational global NWP model of ECMWF. The HRES IFS uses an octahedral reduced Gaussian grid, translating to a resolution from 8 km at the Equator to 10 km at 70

FLEXPART was initially designed to estimate the mesoscale and synoptic dispersion of radio-nuclei from point sources, such as releases during a nuclear accident like Chernobyl. Nowadays, FLEXPART

One of FLEXPART's major applications is in inverse modeling studies for the estimation of regional- and continental-scale emissions of atmospheric compounds

Here, we utilize two versions of FLEXPART in backward mode: FLEXPART-COSMO and FLEXPART-IFS. FLEXPART-COSMO is a version of FLEXPART adapted to the COSMO model

FLEXPART-COSMO is employed at two different spatial resolutions, 7 and 1 km (Sect.

Receptor-oriented FLEXPART simulations were carried out by releasing 50 000 particles at each different receptor continuously over 3 h periods. Particles were then traced back for 8 d for FLEXPART-COSMO-7 and for 4 and 8 d for FLEXPART-COSMO-1 coupled (see below) to FLEXPART-IFS, respectively. Source sensitivities were stored on two different output domains for FLEXPART-COSMO simulations: a larger domain (main, 0.16

If FLEXPART is driven only by COSMO-1 fields, source sensitivities can only be produced for the limited COSMO-1 domain, and any European contributions from larger distances (as from the COSMO-7 domain) would be neglected. To account for this limitation, we offline-nest FLEXPART-COSMO-1 to FLEXPART-IFS in order to continue the integration of the particles in Europe once they leave the COSMO-1 domain

Particle transport in FLEXPART is modeled by a simple zero acceleration scheme,

For simulations with FLEXPART-COSMO-7, we use the original turbulence parameterization of FLEXPART, the Hanna turbulence scheme

As we have already mentioned, FLEXPART was utilized in the backward mode to produce source sensitivities,

If we used the complete output grid of our transport model as the inversion grid, then the size of our sensitivity matrix would be too large to be computationally manageable and the solution probably would be underdetermined depending on the spatial correlation lengths. Fine grids with negligible source sensitivities and very low a priori emissions are also more prone to be assigned negative emissions in typical dipole patterns since we assume Gaussian-distributed errors. To reduce the size of the inversion problem, an irregularly sized inversion grid is introduced that assigns finer (lower) grid cells in areas with larger (smaller) average source sensitivities

Bayesian inverse modeling is employed to statistically optimize the estimates of the variables of interest,

The minimization problem can be solved analytically, since the sensitivity matrix,

Our design of the error covariance matrices,

The block matrix

The matrix

Accurate knowledge of the a priori and observational error covariance matrices,

The main focus of this study is to assess the impact of high-resolution FLEXPART-COSMO-1 simulations on the emission estimates of halocarbons. The transport model resolution is one of the factors which can influence the total inverse emission estimates, their spatial distribution, and their uncertainty. The kind of analytical inversion used here to optimize the emissions was shown to likely underestimate the uncertainty of the a posteriori state vector

Different groups of inversions conducted in this study.

Two versions of FLEXPART are used in this study, FLEXPART-COSMO-7 and FLEXPART-COSMO-1. Figure

We conducted inversions using three different spatial distributions of the a priori emissions,

For some widely used substances, such as HFC-134a, we expect that the usage and hence the emissions mostly follow proxies like population and traffic (HFC-134a in mobile air-conditioning). For other compounds, such as

Different a priori spatial emission distributions – presented on the irregular grid – utilized in the inversions. The population-based a priori can be seen in panel

The different a priori fields used in this study consist of a population-based a priori, a uniform-per-country a priori, and an elevation-dependent a priori. In the population-based a priori, an emission factor represents the average emissions for each person in the country, and the emissions are given by the emission factor multiplied by the number of residents in each grid cell. In the uniform-per-country case, the emissions are distributed uniformly in the whole country, while in the elevation-dependent a priori, the emissions are distributed uniformly per country below an elevation threshold of 1000 m, whereas above that threshold the emissions were set to 5 % of the low-elevation value. Above the elevation threshold, population densities are usually low in the Alps and very few industrial installations are present, suggesting very limited emissions of the current substances of interest. The spatial distribution of the different a priori emissions can be seen in Fig.

As already mentioned, the parameters optimized in the maximum likelihood optimization are the correlation length,

As already mentioned in Sect.

The sensitivity of total Swiss emissions and their spatial distribution to additional observation sites inside and outside Switzerland was further explored. Long-term halocarbon observations are only available from the AGAGE network. We further employed data for Switzerland from the two field campaigns in Beromünster (2019–2020) and Sottens (2021). The sensitivity of the emissions to the inclusion of observations from Beromünster or Sottens, or from both sites, was further explored. In our BASE inversions, the non-Swiss receptors used are TAC in UK and MHD in Ireland. Inversions with additional observations from TOB and CMN were conducted for HFC-134a to test the sensitivity of Swiss emissions to the inclusion of additional sites closer to Switzerland (Table

In our BASE inversions, the total emissions and their spatial distribution represent average values over the whole year; no annual cycle is considered. For refrigerants such as HFC-134a and HFC-125, this assumption can be ambiguous. HFC-134a is mainly used in mobile air-conditioning in cars, but we do not know if the emissions are stronger when the air-conditioning system is in use (mainly in summer months) or if they are at a constant rate independent of the usage. There is some evidence in the literature supporting a seasonal cycle of the emissions

Since running the maximum likelihood optimization for the enlarged inversion problem proved to be computationally too costly, two sensitivity inversions with slightly different covariance settings were performed: one with the covariance parameters taken directly from the outputs of the BASE inversion with maximum likelihood optimization (SEAS1) and one with the model error being determined by an iterative approach (SEAS2), as described in

Finally, the sensitivity of the inversion to the temporal aggregation window of the assimilated observations was assessed. In our BASE inversions, we use observations averaged over 24 h intervals. Since the high-resolution model was shown to improve the simulated representation of the observed diurnal cycle of tracer mole fractions at the BRM tall tower

Swiss halocarbon emissions using the low-resolution model were estimated after the measurement campaign in Beromünster in 2020 and the results are summarized in

Spatial distribution of Swiss HFC-134a a posteriori emissions for the inversion PREL_SITRED1

The same cannot be claimed for observational sites in Switzerland though, since the PREL_SITRED1 inversion changes significantly in terms of both spatial distribution and total emissions when SOT (BASE1) is included (Sect.

Concerning the covariance parameters which were excluded from the maximum likelihood step (Sect.

Estimating the baseline concentration purely from observations and optimizing it by site may not be the best solution to the baseline problem. Alternatively, baseline observations and transport model information can be used to reconstruct a spatially and temporally resolved baseline concentration at the domain boundaries, from which, again with the transport model information, a baseline concentration for each site and time can be sampled

Another factor that is poorly constrained by the maximum likelihood approach is the correlation length,

Furthermore, we investigated whether we obtain additional information from the high-resolution inversions if we use 3-hourly observation aggregates to drive the inversion instead of 24-hourly aggregates, as used for the low-resolution inversions and in previous studies

Finally, we fixed the parameters, which influence the resolution of the inversion grid, to values that lead to similar inversion grids for both FLEXPART model resolutions (PREL_NCEL1 and PREL_NCEL7). However, the total country or total inversion emissions did not show sensitivity to the resolution of the inversion grid (

Currently, HFC-134a is the most often used HFC in Switzerland with reported emissions of 455 Mg yr

Spatial distribution of Swiss HFC-134a a posteriori emissions for the BASE inversion with the 7 km model

A posteriori minus a priori emission differences for HFC-134a for the BASE inversion with the 7 km model

BASE7 inversion leads to an a posteriori estimate of annual Swiss emissions of 260

The same a posteriori emissions distributions but obtained with the high-resolution transport model can be seen in Fig.

If we consider the difference between the a posteriori emissions of the high- and low-resolution model inversions (BASE1 and BASE7), the BASE1 inversion enhances the emissions in all big cities of Switzerland, in the regions with the most industrial activity (canton of Aargau, west-northwest of Zurich), and along the traffic network (Fig.

Statistical measures used to assess the reliability of inversion for different compounds, different transport model resolutions, and different a priori emissions. The table displays the reduced

Figure

Time series of observed (blue lines) and simulated (red and green lines) HFC-134a mole fractions at BRM

A posteriori emission differences between the high- and low-resolution model inversions with population-based a priori for HFC-134a.

A posteriori emissions for all the substances utilized in this study for the different model resolutions and the different a priori choices. All results correspond to the BASE inversions.

For the inversions with uniformly distributed a priori emissions by country (BASE_ED; Figs.

In Figs.

Moreover, the HFC-134a inversions with seasonally variable emissions (SEAS) reveal the existence of a seasonality pattern in the emissions in Switzerland. In both types of seasonal inversions with the high-resolution model (see Sect.

Based on the analysis in this section, we can claim that the high-resolution inversions reconstruct the spatial distribution of the HFC-134a emissions in Switzerland better and with more detail than the low-resolution inversions. The total Swiss emission estimates between the two models differ significantly, with the high-resolution model predicting values closer to those in the inventory. For the remaining halocarbon inversions in this work, we present only the results from population-based a priori and elevation-dependent a priori since the elevation-dependent a priori can be seen as an improved version of the uniform-by-country a priori. Figures for the simulations with a uniform spatial a priori distribution can be found in the Supplement.

HFC-125 is the second most abundant HFC in Switzerland, with reported emissions of 122 Mg yr

Spatial distribution of a posteriori emission for HFC-125

Spatial distribution of a posteriori minus a priori emission difference for HFC-125

The BASE7 inversion yields Swiss a posteriori emissions of 78

For the high-resolution BASE inversion, BASE1, the a posteriori emissions can be seen in Fig.

Additionally, in Figs.

Both the high- and low-resolution inversions are reliable (Table

Difluoromethane or HFC-32 is the fourth most emitted HFC in Switzerland with reported emissions of 57

The BASE7 and BASE1 inversions for the period 2019–2021 yield a posteriori annual emissions of 38

Comparing panel (e) with panel (f) in Fig.

In panels (g) and (h) in Figs.

Sulfur hexafluoride or

The BASE7 and BASE1 inversions for the period 2019–2021 yield a posteriori annual emissions of 7.6

Comparing panels (i) with (j) in Fig.

In panels (k) and (l) in Figs.

This study highlights the importance of employing high-resolution meteorological fields and a dense observational network to inversely estimate national and subnational emissions and their spatial distribution in regions with a complex emission distribution. In our case this is a small country of the order of 40 000 km

Here, we used an analytical Bayesian inversion framework to minimize the observational and a priori error to hence estimate the total Swiss halocarbon emissions and their spatial distribution. We first showed that including additional receptors in the neighboring countries does not affect the total Swiss emission estimates or their spatial distribution. If enough receptors are utilized to constrain the European emissions, then additional receptors – far from the region of interest – do not lead to significant gains in that region itself.

We further investigated how variations in the inversion setup (e.g., inversion grid size, different spatial distribution of a priori emissions, optimization of different covariance parameters during the maximum likelihood step, 3-hourly or 24-hourly observation aggregation periods, seasonal emission variability, additional receptors outside Switzerland) influence the final emission estimates, their uncertainty, and their spatial distribution. While the final emission estimates and their uncertainty did not show any significant sensitivity to most of these parameters, the baseline uncertainty had a significant impact on the final inversion estimate. Future research should focus on comparing inversions using different baseline estimation methods

In contrast to additional receptors far from the region of interest, the inclusion of additional measurements inside Switzerland significantly amended both the total Swiss emission estimates for HFC-134a and partly their spatial distribution. Inversions with the high-resolution model with and without SOT differ by more than 10 % in terms of total Swiss emissions: 307

Inversions solely assessing the effect of the transport model resolution on the Swiss emission estimates and their spatial distribution for HFC-134a showed significant differences across the two model resolutions. The total emission estimate discrepancy was close to 40 % (i.e., 260

Inversions with the same setup for other F-gases (HFC-125, HFC-32,

Our sensitivity inversions with a set of different a priori choices highlight the importance of prior knowledge of the distribution of these emissions on a national level. If we start from an unrealistic distribution, the inversion will not be able to depict the true emissions and their true spatial distribution. This can be seen in our inversions; the results for all HFCs and

Future work should focus on applying high-resolution inversions for other GHGs with biogenic sources and sinks (

Continuous atmospheric halocarbon measurement data for the AGAGE stations are available at the following website:

The supplement related to this article is available online at:

IK carried out the transport model simulations and inverse modeling analysis of Swiss emissions. Measurements at Beromünster and Sottens were taken by DR with support from MKV. SJO'D, DY, KMS, TS, JA, and MKV carried out observations at Mace Head, Tacolneston, Taunus Observatory, Monte Cimone, and Jungfraujoch. The study was designed by IK, SH, and SR and supervised by SH. The paper was written by IK with support from SH and revisions from DR, DB, MKV, SR, LE, and all other co-authors.

At least one of the (co-)authors is a member of the editorial board of

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Funding from the Swiss National Science Foundation within the project IHALOME (Innovation for Halocarbon Measurements and Emission validation) is acknowledged (SNSF, project 20020_175921). Financial support for the measurements at Jungfraujoch has been provided by the Swiss National Programs HALCLIM and CLIMGAS-CH (FOEN), the International Foundation for High Altitude Research Stations Jungfraujoch and Gornergrat (HFSJG), and the Integrated Carbon Observation System Research Infrastructure (ICOS-CH). We thank the personnel operating the Advanced Global Atmospheric Gases Experiment (AGAGE) measurement stations at Jungfraujoch, Tacolneston, Mace Head, Monte Cimone, and Taunus Observatory for conducting, evaluating, and providing the halocarbon measurement data. AGAGE operations are supported by the Upper Atmosphere Research Program of NASA (grant nos. NAG5-12669, NNX07AE89G, NNX11AF17G, and NNX16AC98G to MIT; grant nos. NNX07AE87G, NNX07AF09G, NNX11AF15G, and NNX11AF16G to SIO) and the Department for Business, Energy, and Industrial Strategy (BEIS; grant no. TRN 1537/06/2018 to the University of Bristol for Mace Head and Tacolneston). We acknowledge MeteoSwiss for providing meteorological observations and COSMO model analysis fields. FLEXPART-COSMO calculations were carried out at the Swiss National Supercomputing Centre (CSCS) under project grant s1091.

This research has been supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (grant no. 20020_175921).

This paper was edited by Gabriele Stiller and reviewed by two anonymous referees.