IASI is an infrared Fourier transform spectrometer on board the sun-synchronous polar-orbiting MetOp-A/B/C satellites, which were respectively launched in 2006, 2012, and 2018 (Clerbaux et al., 2009). IASI has a cross-track scanning swath width of ∼2200 km, with a pixel size of ∼12 km in diameter at nadir. Each instrument on board one of the sun-synchronous satellites covers almost all locations over the globe twice a day, once at daytime and once at nighttime, with overpasses around 09:30 and 21:30 local solar time (LST), respectively. The vertical sensitivity of the IASI NH₃ measurements, mainly in the boundary layer where NH₃ is predominantly confined, varies as a function of the thermal contrast between the surface and the atmospheric layers (Clarisse et al., 2010; Di Gioacchino et al., 2024). The NH₃ total column observations from the IASI measurements in the first version were retrieved using the so-called hyperspectral range index (HRI) in an extended spectral range (800–1200 cm⁻¹) and using look-up tables (LUTs) built from forward radiative transfer model simulations (Van Damme et al., 2014). In the subsequent versions, an artificial neural network for the IASI (ANNI) retrieval approach was then developed and used for retrievals of IASI NH₃ total columns (Van Damme et al., 2017, 2021; Whitburn et al., 2016). The ANNI NH₃ retrieval approach uses an assumed Gaussian-shaped vertical profile of the NH₃ volume mixing ratio (the “prior” profile), which is modeled as a function of the altitude above the ground or ocean surface, the peak concentration altitude, and the width of the profile of significant NH₃ concentrations. The peak altitude over land is set at the ground surface with a width equal to the boundary layer height (Clarisse et al., 2023), as the NH₃ emission is generally higher near the surface and NH₃-related chemistry and dispersion cause the concentration to decrease with altitude. Over the ocean, it is set to 1.4 km with a width of 0.9 km (Clarisse et al., 2023). In this study, we use daily NH₃ total columns from a recently released version 4 (ANNI-NH3-v4) of the IASI ANNI retrievals of NH₃ (Clarisse et al., 2023). The most important feature of this new ANNI-NH3-v4 data product is the introduction of the column averaging kernel (AK). The vertical AK is essential for comparison of chemistry transport model simulations against the satellite NH₃ retrievals, which can be used to remove the effect of the prior vertical NH₃ profiles used in the retrievals of the IASI NH₃ total columns in the model–satellite comparison. Note that the NH₃ distribution from IASI-ANNI-v4 is very similar to the ones with the previous version 3, although the values are about 15 %–20 % larger due to the improved setup of the HRI (Clarisse et al., 2023). Furthermore, the ANNI-NH3-v4 data product provides a more accurate characterization of the measurement uncertainty, along with several other changes, resulting in the improved temporal consistency of the IASI NH₃ dataset spanning from 2007 onwards (Clarisse et al., 2023).

We use daily IASI-NH3-v4 NH₃ global observations over land from the MetOp-B satellite from 2019 to 2022. We select only the NH₃ observations from the morning overpass (around 09:30 LST) because of the better precision of morning observations, as IASI is more sensitive at this time of day to the atmospheric boundary layer, where the signature of the surface emissions is higher, owing to more favorable thermal conditions. We use high-quality IASI NH₃ observations only with the cloud coverage lower than and equal to 10 % (Clarisse et al., 2023). We apply pre- and post-retrieval filters that accompany the dataset. The application of these filters removes respectively the observations corresponding to erroneous L1 processing of the spectra or excess cloud coverage and the observations corresponding to measurements with limited or no sensitivity to the measured quantity and retrievals satisfying certain threshold conditions (Clarisse et al., 2023).

We use the global climate–aerosol–chemistry transport model LMDZ-INCA to simulate the global NH₃ concentrations, along with a state-of-the art gas phase tropospheric chemistry scheme as well as aerosols including sulfate, nitrate, black carbon (BC), particulate organic matter (POM), dust, and sea salt. LMDZ-INCA is a coupled model based on an atmospheric general circulation model (GCM) LMDZ V6 (Laboratoire de Météorologie Dynamique) (Boucher et al., 2020; Hourdin et al., 2020), a chemistry and aerosols model INCA V6 (INteraction with Chemistry and Aerosol) (Hauglustaine et al., 2004, 2014), and a global land surface dynamical vegetation model ORCHIDEE (ORganizing Carbon and Hydrology In Dynamic Ecosystems) (Krinner et al., 2005). The model uses a monotonic, finite-volume, second-order parameterization to calculate large-scale advection of water vapor, liquid and solid water, and tracers (Boucher et al., 2020). The model uses the “New Physics” (NP) version of the physical parameterizations, which includes a turbulent scheme based on the prognostic equation for the turbulent kinetic energy (Yamada, 1983), the “Thermal Plume Model” for the convective boundary layer (Rio and Hourdin, 2008), a parameterization for cold pools and wakes resulting from convective rainfall evaporation (Grandpeix and Lafore, 2010), and Emanuel's deep convection parameterization scheme (Emanuel, 1991). LMDZ-INCA interactively accounts for the emissions, transport (resolved and subgrid scales), and deposition (both dry and wet) of chemical species and aerosol, and it incorporates a full chemical scheme for the NH₃ cycle and nitrate particle formation (Hauglustaine et al., 2014).

The LMDZ-INCA model configuration used in this study has a horizontal resolution of 1.27° latitude ×2.5° longitude with 79 hybrid σ-pressure levels within a terrain following vertical coordinate stretches up to 80 km. We conducted LMDZ-INCA spin-up simulations from 2010 to 2018 and then reference simulations for a period of 4 years from 2019 to 2022, which we used for the model comparison with the IASI NH₃ observations and for the global NH₃ emission inversions. The simulations were driven by nudging the GCM winds with a 3.6 h relaxation time to the 6-hourly ECMWF Reanalysis v5 (ERA5) data, regridded onto the LMDZ-INCA model grid. In the LMDZ-INCA simulations, we used the monthly global anthropogenic emission of the chemical species and gases, including NH₃, from the open-source Community Emissions Data System (CEDS) global bottom-up gridded inventories (McDuffie et al., 2020), with an initial horizontal resolution of 0.5° × 0.5°, interpolated onto the model horizontal grid. We used conservative regridding by ensuring that the total mass (e.g., emissions) was preserved during the interpolation. The CEDS global emission inventories provide emissions of NH₃, NO_x, SO₂, NMVOCs, CO, OC, and BC from 11 anthropogenic sectors, including agriculture, energy, on-road and non-road transportation, residential, commercial, waste solvents, international shipping, and others (McDuffie et al., 2020). The CEDS inventory also includes emissions of NO and NH₃ from agricultural soils with both synthetic and manure fertilizers. Because CEDS anthropogenic emissions are available only up to 2019, the CEDS emission fluxes for the post-2019 years were developed based on the combination of the CEDS emissions in 2019 with the carbon emission growth rate from 2019 to the target year. The data on the emissions growth rate were derived from the Carbon Monitor dataset (https://carbonmonitor.org/, last access: 1 August 2024) and calculated by source sector, by month, and by country. This approach to extrapolate emission fluxes based on CO₂ data has been commonly applied to various species, particularly those associated with fossil fuel emissions. This has led to noticeable variations in emissions of species like SO₂ and NO_x, which have been simultaneously used in the LMDZ-INCA simulations with the full chemical scheme for sulfate and nitrate particle formation (Fig. S1 in the Supplement). However, as extrapolation calculations are conducted for each source sector separately and NH₃ emissions mostly come from agricultural activities, which do not emit CO₂ directly, applying this approach to extrapolate NH₃ emissions for the post-2019 years resulted in almost invariant NH₃ emissions after 2019 (Fig. S1). While this approach may seem simplistic for NH₃ fluxes, it was used in this study to construct the spatial distribution of prior emissions, as we expect satellite data to drive year-to-year variations in the final inversion results. Because the anthropogenic emissions are derived from the CEDS inventory at a monthly resolution, they are uniformly distributed in time at the hourly resolution in the input to the LMDZ-INCA simulations, without incorporating diurnal cycles. We used fire emissions from the Global Fire Emissions Database (GFED4) (van der Werf et al., 2017) and biogenic volatile organic compound (VOC) emissions calculated from the ORCHIDEE vegetation model (Messina et al., 2016). Emission fluxes from anthropogenic and natural sources were prescribed to the model as monthly forcing files for different species. We sampled the simulated NH₃ concentration at an hourly frequency over a 4-year period from 2019 to 2022. We used these hourly LMDZ-INCA model-simulated NH₃ data for our analysis and inversions with IASI NH₃ observations from the morning overpass.

The retrievals of NH₃ total column observations, Ωobs, where “obs” stands for the “observed” IASI NH₃ total columns in the IASI-ANNI-NH3-v4 data product, are implicitly dependent on assumed (prior) Gaussian-shaped vertical profiles of the NH₃ volume mixing ratio above the land and sea surfaces (Clarisse et al., 2023). As a result, the comparison between satellite-retrieved and model-simulated column abundances is influenced by the shape of the vertical profile of NH₃ mixing ratios assumed in the retrievals. The total column averaging kernel (AK), as provided in the ANNI-NH3-v4 data product, characterizes the altitude-dependent sensitivity of the retrieved atmospheric column to changes in the true profile (Eskes and Boersma, 2003). The importance of the AK in correctly comparing model simulations with the satellite observations has long been established (Cooper et al., 2020; Douros et al., 2023 for NO_x; Koukouli et al., 2018 for SO₂). There are several possible approaches of comparing model simulations with the satellite observations enabling the model-retrieval comparison to be independent of the assumption on the profiles used in the retrievals (Cooper et al., 2020; Douros et al., 2023; Cao et al., 2022; Ding et al., 2024). Here, we convolved the simulated LMDZ-INCA NH₃ vertical profiles with the IASI NH₃ total column AKs. The convolved LMDZ-INCA model simulation of the NH₃ columns, Ωmod, where “mod” stands for the “modeled” LMDZ-INCA NH₃ total column, is obtained by weighting the vertical integration of the model NH₃ sub-columns (xl) with the averaging kernel (AK_l) (Clarisse et al., 2023; Eskes and Boersma, 2003): 1Ωmod=∑lAKlxl, where the summation over l is over the 14 vertical levels of IASI NH₃ retrievals (on which an assumed NH₃ vertical profile and AKs of retrievals are defined). Here, xl values are obtained by interpolating LMDZ-INCA simulated original NH₃ mole fraction vertical profiles (at 79 levels) onto the levels corresponding to IASI-ANNI-NH3-v4 retrievals (14 levels). The interpolation is performed in a manner that conserves the NH₃ total column amount. The application of the AK to the simulated LMDZ-INCA NH₃ profiles ensures the elimination of an assumed NH₃ profile error contribution to the model–satellite comparison (Boersma et al., 2004; Eskes and Boersma, 2003) and that the model-simulated column is integrated in a way that reflects the retrieval sensitivity.

In order to illustrate the impact of the AK on modeled NH₃ total columns, Fig. 1 shows LMDZ-INCA simulated NH₃ mole fraction vertical profiles over a model grid cell in India on three clear-sky days (24 February, 30 March, 28 October) in 2019 and the modeled NH₃ sub-columns with and without application of the AKs corresponding to one of the IASI pixels in that model grid cell, obtained from the modeled NH₃ mole fraction profile interpolated on the vertical levels of IASI-ANNI-NH3-v4 retrievals. Despite the AK values varying relatively smoothly with altitude above the ground surface, the application of the AK can amplify modeled NH₃ sub-columns at higher altitudes compared to those calculated without the AK (Fig. 1). This effect is generally due to the interaction between the vertical structure of the modeled NH₃ vertical profile and the thickness (or pressure width) of the sub-columns. Because each NH₃ sub-column represents the mass of NH₃ within a specific pressure layer, layers with both significant NH₃ concentrations and wider pressure intervals can result in larger NH₃ sub-column values, even if the AK is not at its peak for those layers (Fig. 1). Consequently, even modest AK values at higher altitudes, combined with substantial NH₃ mass in thick pressure layers, can lead to amplified contributions to the total column. The subfigures in Fig. 1 show that the LMDZ-INCA NH₃ local vertical profiles mostly decrease with altitude and are almost similar to the Gaussian-shaped NH₃ vertical profile centered at the land surface used as a prior in the IASI-ANNI-NH3-v4 retrievals. However, the model-simulated vertical NH₃ profiles for some days (e.g., Fig. 1b) deviate from such a general smoothed NH₃ vertical profile shape assumed in the IASI NH₃ retrievals and show secondary peak(s) at some higher altitude. Although a short-lived species like NH₃ largely resides within the atmospheric boundary layer and the long-term averaged NH₃ vertical distribution in the boundary layer or in the lower troposphere could be assumed as smoothly decreasing with the altitudes, with maximum at the land surface, high-temporal-scale NH₃ vertical profiles corresponding to the IASI overpass time can be a little more complex than this averaged smoothed profile, as observed in both model simulations (Fig. 1b) and aircraft- and surface-based in situ measurements (Cady-Pereira et al., 2024; Guo et al., 2021; Pu et al., 2020). This suggests a potential need to refine the assumed NH₃ vertical profile for more accurate satellite NH₃ retrievals, though the necessity for this refinement may depend on specific locations and meteorological conditions. Across all these days, the application of the AKs results in higher LMDZ-INCA NH₃ total column values compared to the ones without applying the AKs. The AK from the ANNI-NH3-v4 product often exhibits magnitudes exceeding unity at altitudes corresponding to the LMDZ-INCA NH₃ sub-column peak altitudes. This results in larger modeled NH₃ total column values when using the AK.

At a given hourly output of the model simulations with the IASI observations from the morning overpass around 09:30 LST, we derive a corresponding LMDZ-INCA NH₃ profile for each individual IASI NH₃ pixel within a model grid cell that contains the center of this pixel and derive the convolved LMDZ-INCA modeled NH₃ total column by applying the corresponding AK. Because the IASI resolution is much finer than that of LMDZ-INCA, this process yields several convolved modeled NH₃ total columns for a single model grid cell. We then average these resulting observed (Ωobs) and corresponding AK-convolved modeled (Ωmod) NH₃ total columns at the model spatial resolution (1.27° × 2.5°) for a proper comparison at the coarsest resolution between the two products. We exclude the grids of the averaged NH₃ total columns from the analysis if there are fewer than four high-quality IASI pixels within a model spatial grid or if the grid-cell average of observations is negative due to some negative IASI NH₃ total column retrievals.

We use the finite difference mass-balance (FDMB) inversion approach (Cooper et al., 2017; Lamsal et al., 2011) for the global inversion of NH₃ emissions using NH₃ total columns from the LMDZ-INCA model simulations and IASI NH₃ observations. The inversion approach assumes that the short lifetime of NH₃ of a few hours to a day in the atmosphere limits its horizontal transport on coarse grids and thus implicitly conducts local analysis, deriving local surface emissions (in a given model horizontal grid cell) based on local observations (corresponding the same model horizontal grid cell), even though it relies on full 4D (3D in space, 1D in time) simulations with LMDZ-INCA. The FDMB inversion approach relies on the estimation of the local sensitivities (β) of the simulations of NH₃ total columns to changes in the local NH₃ emission, addressing non-linear chemistry effects from the model simulations. It derives NH₃ emission estimates at each grid cell by scaling a priori NH₃ emission (here based on the anthropogenic emissions from the CEDS inventory), considering the local sensitivity of NH₃ simulations to changes in emission and the relative difference between the observed and modeled NH₃ total columns. Our objective is a daily estimate of 10 d running mean global anthropogenic NH₃ emissions over land. However, with only satellite NH₃ observations, it is challenging to distinguish between anthropogenic and natural sources. Therefore, our approach focuses solely on grid cells and days where and when the prior NH₃ emission inventory indicates that the emissions are dominated by the anthropogenic sources and where and when we have retained grid-cell averages of the IASI NH₃ observations (see Sect. 2.3). We use the daily combined anthropogenic NH₃ emissions from CEDS and fire emissions from the GFED4 inventories, which are derived from monthly data and uniformly distributed at the hourly scale within each day in the LMDZ-INCA simulations, as a priori emissions (Ea) in the inversions. We select the grid cells with dominating anthropogenic NH₃ emissions by identifying those where the ratio of anthropogenic NH₃ emissions to total NH₃ emissions (including anthropogenic, biogenic, and fire NH₃ emissions) is greater than 0.6. This selection of dominant anthropogenic emissions slightly alters their spatial distribution over the years from 2019 onward due to variations in fire emissions across different years. We compute a 10 d running average at each grid cell of the modeled and observed NH₃ total columns and of the a priori emissions to smooth out the daily fluctuations in observed NH₃ total columns and to increase the sample size and spatial coverage of the daily flux estimates. Following Cooper et al. (2017) and Lamsal et al. (2011), for a given day and over each model horizontal grid cell, the satellite-constrained NH₃ emission estimates (EIASI) using the observed IASI NH₃ total columns (Ωobs) and the modeled LMDZ-INCA columns convolved with the AKs (Ωmod) corresponding to a priori NH₃ emission (Ea) used in the model simulations are calculated as: 2EIASI=Ea1+βΩobs-ΩmodΩmod, where a unitless scaling factor β accounts for the local sensitivity of the modeled NH₃ total columns (ΔΩmod/Ωmod) to perturbations of the a priori NH₃ emissions (ΔEa/Ea) and is defined as: 3β=ΔEa/EaΔΩmod/Ωmod. We perform two LMDZ-INCA model simulations for each year: one using the prior emissions, with the anthropogenic NH₃ emissions from the CEDS bottom-up inventory for the year 2019, updated for subsequent years (see Sect. 2.2), and another with a 40 % reduction in the CEDS anthropogenic NH₃ emissions to derive β. We apply some filters to β, to the observed and/or the modeled NH₃ total columns, and/or to the bottom-up emissions to select the grids corresponding to the dominating anthropogenic emissions and to avoid negative or extreme unrealistic estimates of the NH₃ emissions from the inversions. We select grids over land only for (i) 0≤β≤10, (ii) βΩobs-ΩmodΩmod≥-1, and (iii) Ωmod and Ωobs>1×1015 molecules cm⁻². Figure S2 in the supporting information shows an example of the distribution of monthly mean values of β for July 2019. The values of β are less than 1.5 over most of the major NH₃-emitting land regions worldwide.

Satellite data gaps and some filters applied to observations and different variables in the FDMB inversion approach to focus on model grid cells dominated by anthropogenic NH₃ emissions result in numerous grids or days where NH₃ emissions could not be derived directly from the IASI NH₃ observations. Therefore, the derivation of national or regional budgets of anthropogenic emissions at daily (10 d scale) to monthly and annual scale from the satellite observations requires a proper gap-filling of grid cell or days for which the inversion protocol does not yield emission estimates. To fill these gaps in IASI-constrained NH₃ emissions, we use a rather conservative approach utilizing IASI-constrained NH₃ emissions and the corresponding a priori CEDS anthropogenic NH₃ emissions used in the inversions. The gap-filling is performed over some specific regions. In order to gap-fill the daily unconstrained NH₃ emissions, we compute a daily scaling factor as a ratio between the IASI-constrained and the corresponding CEDS anthropogenic NH₃ emissions integrated over a specific region. The missing emissions in that selected region are gap-filled by multiplying for each corresponding grid cell the CEDS NH₃ emissions with these scaling factors. For a given day, when the spatial coverage of the IASI-constrained anthropogenic NH₃ emissions is less than 60 % in a specific region due to poor satellite coverage and due to other data filtering to apply the FDMB inversion approach, we apply some constraints on the scaling factor to prevent spurious gap-filled emissions. If the IASI-constrained emissions coverage is less than 10 %, we directly use the prior CEDS NH₃ emissions. For coverage between 10 % and 40 %, we cap the scaling factor at 1.25, and for coverage between 40 % and 60 %, we cap it at 1.5. For the gap-filling, we use 10 continental regions (illustrated in Fig. S3) over the main land worldwide as defined by Ge et al. (2022) based on 58 IPCC reference regions representing consistent regional climate features described in Iturbide et al. (2020). Ge et al. (2022) used the nine regions (except the “rest of the world” region) to access global and regional budgets and fluxes of atmospheric reactive N and S gases and aerosols. The fraction of the IASI-constrained and the gap-filled NH₃ emissions per season across six regions for each year from 2019 to 2022 in Fig. S4 shows that the gap-filling of emissions over most of the regions is mostly higher during winter and minimum during spring. However, in some regions such as India and Africa, the percentage of the gap-filled emissions to the total seasonal emissions is higher in summer compared to other seasons due to relatively smaller numbers of satellite observations, caused by higher cloud coverage during the monsoon season. The overall percentage of the gap-filled NH₃ emissions to the total emissions worldwide is maximum (up to ∼28 %) during winter and minimum (up to ∼11 %) during spring, and it ranges from ∼16 % to 19 % during summer and autumn (Fig. S4). However, because the attribution of the NH₃ emissions in winter to the total annual emissions is smaller compared to the other seasons, the total gap-filled emissions in winter are still lower than in the other seasons (Fig. S5).

We start by comparing the LMDZ-INCA model-simulated NH₃ total columns driven by the prior emissions and convolved with the AKs against the IASI NH₃ observations, with first a worldwide overview and then some focuses on regions over land. In addition to assessing global and regional mean comparisons between the modeled and the observed IASI NH₃ columns, we also calculate the Pearson's correlation coefficient (r) and root mean square error (RMSE) between the annual or monthly mean simulated and observed values at the model grid level as part of our comparative analysis (shown in Figs. 2 and 3 for 2019 and Fig. S7 for all years from 2019 to 2022).

Figure 2 compares the annual mean modeled LMDZ-INCA NH₃ columns (Ωmod) with the observed IASI NH₃ column retrievals (Ωobs) regridded on the LMDZ-INCA model grid (1.27° × 2.5°) worldwide over land for the year 2019 (Fig. S7 for all 4 years from 2019 to 2022). It shows that the annual mean worldwide spatial distributions of the modeled NH₃ columns are approximately similar to those of the IASI NH₃ retrievals and that there is a good spatial correlation (r=0.71) between them. However, the IASI NH₃ observations indicate higher NH₃ abundance compared to the LMDZ-INCA simulations across most of the regions worldwide, except over the South Asia and Eastern Siberia regions (Fig. 2). We observe an overall underestimation of the global annual mean LMDZ-INCA NH₃ columns Ωmod (mean: 0.33×1016 molecules cm⁻²) compared with the observed IASI retrievals Ωobs (mean: 0.54×1016 molecules cm⁻²). The RMSE between the annual mean gridded Ωmod and Ωobs worldwide is 0.52×1016 molecules cm⁻².

Emphasizing the regional analysis, in Fig. 3, we found that the modeled NH₃ total columns are lower than the IASI NH₃ observations over most of the selected regions, except over the Indian region (also Southeast Asia, not shown; see Fig. 2), and also over a region in Eastern Siberia, where the model shows an overestimation of the observations (not shown, but see Fig. 2). The annual regional mean of monthly Ωmod over the China, Africa, Europe, South America, and North America regions are respectively ∼4 %, ∼52 %, ∼53 %, ∼58 %, and ∼70 % smaller compared to Ωobs (Fig. 2). However, over the Indian region, the annual regional mean of Ωmod is ∼44 % larger than Ωobs. The monthly regional mean time series of the IASI NH₃ observations in Fig. 3 show that the NH₃ columnar abundance over most of the regions is higher during spring and/or summer months compared than in winter. These elevated NH₃ columns observed during spring and/or summer months compared to winter months can be attributed to increased agricultural activities, particularly the prominent use of N-fertilizers in crops during warmer seasons. High NH₃ concentrations are also influenced by temperature, as warmer temperatures can enhance NH₃ volatilization from soils and agricultural surfaces (Sutton et al., 2013). This synergistic effect of agricultural practices and temperature contributes to the seasonal variation in NH₃ emissions, with higher concentrations during spring and/or summer months.

The monthly regional mean modeled NH₃ columns in Fig. 3 mostly follow the seasonal variation of the IASI observations over the South American and African regions, as well as over the European region to some extent. However, for other remaining regions, especially over the Indian, Chinese, and Middle East (not shown) regions, the seasonality of the modeled NH₃ columns largely deviates from the observations, and we see a large scatter between the monthly mean gridded modeled and observed NH₃ columns (Fig. 3a and b). Over the Indian region, the model shows two main peaks, with the highest peak in May following a secondary smaller peak in September, whereas the IASI observations show the highest peak in July and a smaller one in April (Fig. 3a1). The high NH₃ loading from the IASI observations over the Indian region from June to August with a maximum peak in July and a secondary, much smaller peak in April (Fig. 3a1) is consistent with the cropping cycle (Kuttippurath et al., 2020), high usage of the N-fertilizers, and high temperature during these monsoon and summer months in the Indo-Gangetic Plain (IGP) region spanning the banks of the Indus and Ganges rivers and their tributaries (Beale et al., 2022). However, as mentioned before, the variation and two distinct peaks in the modeled NH₃ columns is similar to the variation and peaks in the anthropogenic NH₃ emissions used in the model simulations (Fig. 3). Similarly, over the Chinese region, the observed NH₃ columns show the highest peak in July, which is not captured by the simulations that show the maximum peak in May, followed by a small peak in September. In these regions, because of differences in seasonal variations between the modeled and observed NH₃ columns, we see weak spatial correlations between the monthly mean observed and modeled gridded NH₃ columns (Fig. 3) that are smaller than in other regions like Africa, South America, and Europe, where the seasonality in both the modeled and observed NH₃ total columns is roughly similar.

Figure 3 also shows the seasonal cycles in the regional anthropogenic (CEDS) and fire (GFED4) emissions from the global emission inventories used in the model simulations. Over some regions like South America, North America, and Africa, fire-related NH₃ emission has a visible contribution to this seasonal variation in total emissions, whereas over the India, China, and European regions, this attribution is very small (Fig. 3). This finding shows that the seasonality in the modeled NH₃ total columns mostly varies with the seasonality in the combined anthropogenic and fire-related NH₃ emissions over these regions (Fig. 3). Therefore, the seasonality differences between the model and observations over some regions are mostly due to the different seasonality embedded in the prior NH₃ emissions used for the model simulations (Fig. 3). The model comparison analysis for other years from 2020 to 2022 shows a similar behavior of the modeled and observed NH₃ columns. Notably, the seasonality of anthropogenic NH₃ emissions in the CEDS inventory is mainly derived according to the European agricultural practices based on the ECLIPSE v5 model, which leads to NH₃ emission peaks mostly in May and September corresponding to the application of fertilizers before planting and after harvesting the crops (Beale et al., 2022). However, this seasonal variation of the NH₃ emissions in CEDS may not accurately reflect the diverse agricultural practices in other regions like India, China, and the Middle East (Fig. 3) (Beale et al., 2022; Chen et al., 2023a; Kuttippurath et al., 2020). This is clearly evident from the large difference in the seasonal variations between the IASI NH₃ observations and LMDZ-INCA model simulations over these regions, as the model is dominatingly driven by the CEDS anthropogenic NH₃ emissions in these regions (Fig. 3). This dependency on European seasonality in CEDS inventory NH₃ emissions for other major agricultural NH₃-emission regions with diverse agricultural practices, like India and China, requires region-specific data to improve the accuracy of emission inventories. For some regions like South America, Africa, and North America, the observed IASI NH₃ total columns show high values during specific periods, which is mainly attributed to the heightened NH₃ loading resulting from biomass burning from wildfires in these regions. The underestimation and/or distinct seasonality of the modeled NH₃ columns compared to the observed IASI NH₃ retrievals over different regions indicate biases and/or differential seasonality in the prior NH₃ emissions from the inventories over these regions.

Previous validation studies of earlier IASI ANNI NH₃ retrieval products (e.g., with version 3) showed relatively good agreement with in situ and FTIR measurements (Guo et al., 2021; Wang et al., 2020). Although, the IASI-ANNI-NH3-v4 product introduces important improvements compared to the earlier versions and expects minimal biases, a comprehensive validation of this version has not yet been conducted, though such a validation is anticipated in upcoming studies (Clarisse et al., 2023). Therefore, the bias between the IASI NH₃ columns and LMDZ-INCA model simulations mainly reflects an underestimation of agricultural NH₃ emissions in the prior CEDS inventory, as well as a misrepresentation of their seasonal variation, particularly in the major agricultural regions. These limitations in the prior CEDS NH₃ emissions propagates into the model-simulated NH₃ columns. However, the elevated NH₃ columns observed by IASI during non-growing seasons in regions such as Europe and North America may also be influenced by retrieval uncertainties related to surface temperature effects and low thermal contrast. Therefore, we cannot fully rule out remaining retrieval uncertainties in the absence of comprehensive validation of this version of the IASI NH₃ retrievals.

In order to validate our atmospheric inversion approach (more specifically, to validate the linear approximation of the atmospheric chemistry model based on a single perturbed emission simulation) and strengthen our confidence in the NH₃ emission estimates, we have conducted a LMDZ-INCA model simulation using the IASI-constrained NH₃ emission estimates derived from our global inversions for the year 2019 and compared the simulated NH₃ total columns with the IASI NH₃ total column observations. As the current LMDZ-INCA model framework only reads NH₃ emissions at monthly resolution and uniformly distributes them across hours without incorporating diurnal or day-to-day variability (see Sect. 2.2), our model simulation for this evaluation uses the monthly average of the daily (at 10 d scale) inversion estimates rather than 1 d resolution inputs. However, this does not limit our capability to evaluate the inversion estimates based on comparisons to monthly and annual averages of the observations.

At the annual scale globally, the spatial correlation coefficient (r) between the yearly mean model-simulated NH₃ total columns over the model horizontal land grid cells at 1.27° × 2.5° resolution and corresponding IASI NH₃ observations improve from 0.71 (using prior emissions) to 0.90 (using IASI-constrained NH₃ emissions), while the RMSE decreases by ∼29 % from 0.52×1016 to 0.37×1016 molecules cm⁻² (Fig. S8a). Similarly, at the monthly scale globally, the r value and RMSE between the model simulations with the IASI-constrained NH₃ emissions and the IASI observations improve from 0.51 (using prior emissions) to 0.83 (using IASI-constrained NH₃ emissions), while the RMSE decreases by ∼34 % from 0.88×1016 to 0.58×1016 molec. cm⁻² (Fig. S8b). The LMDZ-INCA simulation driven by the IASI-constrained NH₃ emissions reduces the mean fractional bias (FB) globally from -0.87 to -0.37 at the annual scale and from -1.07 to -0.63 at the monthly scale, compared to the simulation using the prior CEDS NH₃ emissions (Fig. S8).

At the monthly scale and across major NH₃ regions, including India, China, Africa, Europe, South America, and North America, the spatial correlation coefficients (r) and RMSE between the model simulations with estimated NH₃ emissions from inversions and the IASI observations are respectively much higher and smaller than when the simulations are based on the prior CEDS anthropogenic NH₃ emissions (Fig. 4). The spatial correlation coefficient (r) between the monthly mean IASI-constrained NH₃ emissions' model simulations of the NH₃ total columns over the model horizontal land grid cells at 1.27° × 2.5° resolution and the corresponding IASI NH₃ observations exceeds ∼0.8 in most of the regions for this 2019 validation analysis (Fig. 4). In one of the major NH₃-emission regions, i.e., India, at the monthly scale, the spatial correlation increases from 0.40 to 0.86, and RMSE reduces by ∼50 % from 3.83×1016 to 1.91×1016 molec. cm⁻² (Fig. 4). Similarly, over another major NH₃-emission region, i.e., China, at the monthly scale, the spatial correlation increases from 0.40 to 0.79, and RMSE reduces by ∼27 % from 1.19×1016 to 0.87×1016 molec. cm⁻² (Fig. 4). These findings demonstrate the general improvement brought about at different spatiotemporal scales by the update of the emission estimates from our inversions and thus the internal consistency of our global inversion framework despite the rather simple linearization of the chemistry transport underlying it. This improvement of the fit to the IASI NH₃ observations is a strong indication of the robustness of our inversion-based estimate of the global NH₃ emissions. The FB metric quantitatively confirms bias reduction in the modeled NH₃ columns regionally when using IASI-constrained NH₃ emissions in the model simulation compared to the prior CEDS NH₃ emissions (Fig. S9). Specifically, we observe a clear decrease in FB across all regions, except for India. In the case of India, although the FB remains slightly elevated, the RMSE shows substantial improvement, indicating better representation of the magnitude and the spatial and temporal variability, even if the mean offset is not fully corrected from our inversion estimates.

In the subsequent subsections, we present and discuss the gap-filled global daily (10 d scale) NH₃ emission estimates integrated on different temporal and spatial scales. Over the 4-year period of our emission estimates, we present global and regional annual budgets, including the mean emissions over this period, with the range defining minimum and maximum annual emissions, as well as the variation of the regional estimates at different temporal scales ranging from daily (10 d scale) to monthly, seasonal, and annual.

In this section, we compare our IASI-inverted NH₃ emission estimates with other global and regional bottom-up inventories, as well as with other available NH₃ emission inversion estimates reported in recent literature. We use two global bottom-up NH₃ emission inventories: (i) CAMS-GLOB-ANT v6.2 (developed by combining the CEDSv2 emission trends and temporal profiles from CAMS-GLOB-TEMPO and EDGAR v6 historical monthly NH₃ emission data up to 2018) 0.1° × 0.1° monthly dataset (Granier et al., 2019; Soulie et al., 2024) from 2019 to 2022 and (ii) the process-based agricultural and natural soil NH₃ emissions from the Calculation of AMmonia Emissions in ORCHIDEE (CAMEO) model at 1.27° × 2.5° horizontal and monthly temporal resolutions (Beaudor et al., 2023). CAMEO simulates NH₃ sources from the agricultural sector, from livestock manure management (from animal housing and manure storage to grazing) to synthetic and organic nitrogen application to soil. Because CAMEO emissions are not limited only to cultivated/livestock areas and are dynamically dependent on environmental conditions and atmospheric deposition, emissions from natural ecosystems are also exploited in this study. For these inter-comparisons, we regridded the global NH₃ emissions from the bottom-up inventories on the grids (1.27° × 2.5°) of our estimated emissions. We also sub-sampled the monthly emissions from the bottom-up inventories on the common grids corresponding to the IASI-constrained monthly NH₃ emissions derived from the daily (at 10 d scale) estimates. Note that CAMEO additionally includes natural soil NH₃ emissions, whereas CAMS emissions do not include them and provide only anthropogenic NH₃ emissions.

The 4-year (2019–2022) average of the global annual anthropogenic NH₃ emissions from the CAMS bottom-up inventory (∼52.5 Tg yr⁻¹), sub-sampled on the common grids where the IASI-constrained monthly emissions are available, is lower than the prior CEDS anthropogenic NH₃ emissions (∼60.5 Tg yr⁻¹), whereas global annual NH₃ emissions from CAMEO from the combined agricultural and natural soil sectors (∼71.1 Tg yr⁻¹) are higher than those from both CEDS and CAMS. Therefore, we have an even larger relative difference between the estimated and the CAMS emissions than the relative difference between the estimated and CEDS emissions (Fig. 9). However, this relative difference between the estimated and CAMEO's combined agriculture and natural soil NH₃ emissions is smaller compared to the relative difference between the estimated and CEDS. The 4-year-averaged global annual NH₃ emissions from the inversions are ∼1.8 times higher than the CAMS anthropogenic NH₃ emissions and ∼1.4 times higher than the CAMEO combined agriculture and natural soil NH₃ emissions. Figure 9 shows a comparison between the IASI-inverted annual emissions and the corresponding CAMS and CAMEO emissions over six regions (and over the Middle East in Fig. S12) and across 4 years, revealing consistently higher IASI-constrained NH₃ emissions compared to these global bottom-up inventories.

We also compare our estimates with the recent global NH₃ inversion emission estimates by Luo et al. (2022) based on a previous version of IASI NH₃ observations from 2008 to 2018, with the recent estimates from Dammers et al. (2022) derived using the CrIS observations from 2013 to 2020, and with some other regional inversion estimates. Luo et al. (2022) estimated global annual NH₃ emissions at ∼78 (70–92) Tg yr⁻¹ averaged over a period from 2008 to 2018, and Dammers et al. (2022), over a period from 2013 to 2020, had 216.6±66.2 Tg yr⁻¹ (for all detected source locations) and 74.1±17.7 Tg yr⁻¹ (for inventory-identified source locations). Our averaged global annual NH₃ emission estimates of ∼97 (94–100) Tg yr⁻¹ from 2019 to 2022 are ∼25 % higher than the average total estimates (∼78 Tg yr⁻¹) from Luo et al. (2022). This can partly be explained by the fact that the IASI version 4 NH₃ column values used in this study are also about 10 %–20 % higher than the earlier version 3 (Clarisse et al., 2023) used by Luo et al. (2022) due to a reduction of the retrieval biases. This also has to be explained by the use of a different inversion approach, of a different chemistry transport model, and of AKs from IASI NH₃ observations to model-simulated NH₃ columns in this study. Our estimates align more closely with the upper range (∼92 Tg yr⁻¹) of their emission estimates obtained by setting a 200 % perturbation to the modeled atmospheric NH₃ lifetime in their inversions. It should be noted that Luo et al. (2022) corrected their NH₃ emissions over the Indian and the East China regions during 2013 to 2018, which were impacted by the rapid changes in SO₂ emissions and concentrations in these regions, especially the rapid decrease in SO₂ emissions over China. A decrease in SO₂ emissions leads to an increase in NH₃ concentrations/columns in the troposphere because lower SO₂ levels reduce the formation of ammonium sulfate aerosols, leaving more free ammonia in the atmosphere, which increases its concentration in the air (Luo et al., 2022). This correction in Luo et al. (2022) leads to a small increase in NH₃ emissions over the Indian region. However, a substantial reduction of ∼7–8 Tg for the year 2018 is observed over the East China region. Without any correction for SO₂ trends, our estimates (for 2019) are closer to their estimates for the year 2018. In contrast, our average total global estimate of ∼97 (93.8–99.9) Tg yr⁻¹ for the period 2019–2022 is ∼2.2 times smaller than the 216.6±66.2 Tg yr⁻¹ total from the sum of all detected source estimates from Dammers et al. (2022). Additionally, our 4-year-averaged estimates are ∼ 31 % higher when comparing with their estimates (74.1±17.7 Tg yr⁻¹) corresponding to the sources in the CAMS-GLOB-ANT v4.2 inventory emissions above the detection limit of their satellite-constrained emissions.

In order to compare our regional NH₃ emissions, derived from the global inversion estimates, with those of Luo et al. (2022), we regrid their final inversion year (2018) estimates to match the spatial resolution (1.27° × 2.5°) of our estimated NH₃ emissions. Subsequently, we integrate both the emission estimates over the identical grids on common selected regions' domains over land and compare their final inversion year's (2018) NH₃ emissions with our nearest first inversion year (2019) estimates. In comparison with Dammers et al. (2022), their regional estimates for all detected source locations are consistently higher than our estimates. Therefore, in the subsequent comparison analysis, we compare our estimates with only their regional reported estimates corresponding to the sources with inventory emissions above the detection limit of their satellite-derived emissions. This comparison is consistent, as our estimates also required information on the prior CEDS NH₃ emissions, and for the missing sources with zero emissions in the bottom-up inventory, our inversion will not detect any new emission sources. Over the Indian region, our annual estimates of 2019 (∼15.4 Tg yr⁻¹) are closer to the estimates of 2018 (∼13.1 Tg yr⁻¹) from Luo et al. (2022), representing a marginal ∼18 % increase. Our estimates over the China region of 2019 (22.3 Tg yr⁻¹) are much higher (∼73 %) compared to the Luo et al. (2022) SO₂ trend-corrected NH₃ emissions (∼13 Tg yr⁻¹); however, these are closer to their estimates without correction. Recently, Liu et al. (2022) estimated 21.6 Tg NH₃ yr⁻¹ (≡17.77 Tg N yr⁻¹) annual emissions over China for the year 2019 using satellite data, and our estimates (22.3 Tg yr⁻¹) for the same year are comparable to these inversion estimates. Dammers et al. (2022) reported ∼35 Tg yr⁻¹ average NH₃ emissions for the Asia region, and our combined 4-year-averaged estimate of ∼43 Tg yr⁻¹ from India, China, and the Middle East regions is ∼23 % higher than their estimate. Our estimates for Africa (∼13.8 Tg yr⁻¹), South America (∼9.8 Tg yr⁻¹), and the Middle East (∼4.4 Tg yr⁻¹) regions for 2019 agree well with the Luo et al. (2022) estimates (11.1, 10.5, and 4.1 Tg yr⁻¹, respectively) of 2018 within ∼24 %, ∼6 %, and ∼6 %, respectively. For the South American region, our annual estimate of ∼9.8 Tg yr⁻¹ for 2019 agrees well with the estimate of 9.1 Tg yr⁻¹ from Dammers et al. (2022). Our estimates (11.6 Tg yr⁻¹) for 2019 over the North American region are ∼55 % higher than ∼7.5 Tg yr⁻¹ from Luo et al. (2022); however, they are comparable to the total estimates of 12.2 Tg yr⁻¹ from Dammers et al. (2022). Recently, Sahoo et al. (2024) constructed a high-resolution gridded (0.1° × 0.1°) emission inventory of NH₃ emissions over India for 2022 by including 24 regional major and minor anthropogenic sources. They estimated 10.54 Tg yr⁻¹ of NH₃ emissions in 2022, which are closer to the CAMS anthropogenic NH₃ emissions, while our inversion estimates of 14.4 Tg yr⁻¹ NH₃ emissions for the same year are ∼ 36 % higher than their estimates (Fig. 9b). However, in this comparison analysis over the Indian region, our selected domain is larger, encompassing most of South Asia, compared to the India-only domain considered in Sahoo et al. (2024).

Over the European region, our annual NH₃ estimate (∼ 7.7 Tg yr⁻¹) for 2019 is ∼91 % higher compared to ∼ 4.1 Tg yr⁻¹ from Luo et al. (2022) for 2018. However, our 4-year-averaged annual estimates (∼7.9 Tg yr⁻¹) are ∼ 29 % smaller than ∼11.1 Tg yr⁻¹ from the estimates of Dammers et al. (2022). The European Union (EU) emission inventory report (EEA Report No 4/2023, 2023) reported comparatively lower NH₃ emissions for the EU 27 member states of 3.5, 3.4, and 3.3 Tg yr⁻¹ for 2019, 2020, and 2021, respectively, which are much lower compared to our estimates for these years. Also, some other recent top-down inversion studies, such as Tichý et al. (2023), have obtained a similar order of magnitude of the emissions (4.3 and 4.0 Tg yr⁻¹ for 2019 and 2020, respectively) using the CrIS satellite observations from Luo et al. (2022) (4.1 Tg yr⁻¹ for 2018) or from EEA Report No 4/2023 (2023). However, our estimates are comparable to the NH₃ emissions derived from a recent regional atmospheric inversion over Europe at 0.2° × 0.2° horizontal and monthly temporal resolutions over a 3-year period from 2020 to 2022, derived within the EU project Sentinel EO-based Emission and Deposition Service (SEEDS) (https://www.seedsproject.eu/data/monthly-nh3-emissions, last access: 7 August 2023) (Ding et al., 2020, 2024). In this regional atmospheric inversion, NH₃ emissions over Europe were derived by the DECSO (Daily Emissions Constrained by Satellite Observations) v6.2 algorithm, developed to derive emissions of short-lived species based on an extended Kalman filter approach and using CrIS (NOAA-20) observations (Ding et al., 2020, 2024). Our annual NH₃ emission estimates integrated over the common European domain [10° W–30° E, 35–55° N] of their inversions, amounting to 8.8, 8.4, and 8.4 Tg yr⁻¹ for the years 2020, 2021, and 2022, respectively, are in good agreement (within ∼1 %–8 %) with 8.2, 8.4, and 8.6 Tg yr⁻¹ derived for the same years in the SEEDS NH₃ emission inversions. The SEEDS NH₃ emission estimates over Europe indicate an increasing trend of ∼0.2 Tg yr⁻¹ over a 3-year period from 2020 to 2022. In contrast, our inversion estimates show a peak in 2020, with comparatively slightly lower values in the subsequent years (Fig. 9d).

This comparison analysis shows that our inversion estimates of NH₃ emissions integrated at global or regional spatial scales are within the range of other previous inversion estimates derived based on different satellite observations and different inversion approaches. When comparing our IASI-based inversion estimates with some of those derived from CrIS observations, the differences in satellite overpass times (IASI ∼09:30 LST, CrIS ∼13:30 LST) could also lead to differences in retrieved NH₃ due to the potentially strong and quite uncertain diurnal variability in NH₃ emissions and atmospheric concentrations and retrieval approaches. However, in the current setup of our model LMDZ-INCA, the anthropogenic NH₃ emissions are derived from a 1-month-resolution inventory that is uniformly distributed in time at the hourly resolution, without incorporating diurnal cycles. This lack of diurnal variations in the input prior emissions could indeed enhance the discrepancies between IASI- and CrIS-based emission estimates. In a study by Dammers et al. (2019), they utilized both IASI and CrIS satellite observations to estimate NH₃ emissions, lifetimes, and plume widths from major agricultural and industrial point sources. Their findings indicate that CrIS-derived NH₃ emission estimates are, on average, slightly higher than those obtained from IASI-A and IASI-B observations. However, these differences remain within the overall uncertainty range of the estimates. The differences in the emissions from CrIS and IASI could be due to the bias between the satellite NH₃ retrievals, as well as the potential influence of the different overpass times of these satellites in combination with the strong diurnal cycles of the emissions. Overall, our estimates, as well as these other inversion estimates, are higher compared to the NH₃ emissions from different global or regional bottom-up inventories, which tend to support the assumption that there is a general underestimation of the emissions in the inventories. The bottom-up inventories do not accurately capture the seasonality of NH₃ emissions in relation to the agricultural and crop activity cycles in some regions like India, China and the Middle East. In contrast, our inversion estimates demonstrate a seasonality that is consistent with the crops and agriculture cycles in these regions.

The strict restrictions imposed during the COVID-19 lockdown periods in the year 2020 across different regions/countries/cities around the world resulted in major changes in anthropogenic activities, atmospheric concentrations, and emissions of different air pollutant species like NO_x and SO₂. However, atmospheric NH₃ concentration and emissions received comparatively less attention compared to NO_x or SO₂, and only a few studies analyzed the impact of COVID lockdowns on ambient NH₃ concentrations. Most of the air pollutants like NO_x and SO₂ show a decline in their atmospheric concentrations and emissions during the COVID-19 lockdown periods (Zheng et al., 2021). The decline in NO_x and SO₂ concentrations in the atmosphere during the COVID-19 lockdowns led to a reduction in the formation of ammonium nitrate and ammonium sulfate aerosols from atmospheric ammonia and hence a decrease in the atmospheric sink of NH₃. Meanwhile, agriculture activities remained mostly unchanged during the COVID-19 lockdown periods. These factors, along with changes in meteorology and atmospheric composition, may have impacted ammonia levels in the atmosphere. A recent study by Kuttippurath et al. (2024) showed that the global atmospheric ammonia concentration increased anomalously almost everywhere around the world during the COVID-19 lockdown periods in the year 2020 compared to the previous year 2019. Some other studies at regional or city scale, e.g., Xu et al. (2022) (China), Viatte et al. (2021) (Paris, France), and Lovarelli et al. (2021) (Lombardy region in Italy), also reported an increase in ammonia concentration in the atmosphere during the COVID-19 lockdown periods in 2020. Recently, Evangeliou et al. (2025) conducted inversion estimates of NH₃ emissions based on satellite observations during the COVID-19 lockdowns in Europe and showed that the NH₃ emissions decreased by ∼9.8 % in the first half of 2020 compared to 2016–2019. However, overall atmospheric ammonia levels increased due to reduced chemical removal from lower SO₂ and NO_x emissions and the persistence of agricultural activity (Evangeliou et al., 2025). In this study, we analyzed the changes in estimated daily (at 10 d scale) NH₃ emissions from our global inversions during COVID-19 major lockdowns in 2020 compared to the estimates during the same period in pre-COVID year 2019 over six regions across the world.

From our atmospheric inversions, we observe that the annual NH₃ emissions worldwide and across all the selected six regions in the COVID-19 lockdowns in the year 2020 are higher compared to those in the pre-COVID year 2019 (Figs. 6 and 9). Lockdown periods varied across different regions, countries, and cities. However, following the first lockdown in China in the second-to-last week of January 2020, the majority of the first major lockdowns worldwide were implemented between March and May during that year. We defined the lockdown periods in 2020 using the most consistent common dates that aligned with the major lockdowns in each region. Figure 10 compares the estimated daily NH₃ emissions time series and total NH₃ emissions during the COVID-19 lockdown periods in 2020 with the estimated NH₃ emissions during the corresponding period in pre-COVID year 2019 across six regions. Daily (at 10 d scale) variation of the NH₃ emissions during the lockdown periods in 2020 is mostly higher compared to that in the same period in 2019 (Fig. 10). The total NH₃ emissions across these regions in 2020 during the lockdown periods increased by a minimum of ∼5 % (in China) to a maximum of ∼37 % (in South America) compared to the total emissions in this period in 2019 (Fig. 10). The total NH₃ emissions during the lockdown periods in 2020 compared to 2019 across India, Africa, North America, and Europe increased by ∼10 %, ∼6 %, ∼9 %, and ∼16 %, respectively.

The increase in NH₃ emissions from our global inversions during the COVID-19 lockdown periods in 2020 across different regions, compared to the pre-COVID year 2019, raises uncertainty about whether this rise is due to an increase in NH₃ emission sources, due to the impact of meteorology on NH₃ volatilization, or due to a decrease in the atmospheric sink of NH₃ due to the decline in NO_x and SO₂ emissions and concentrations during the lockdowns. However, an increase in NH₃ emission sources during these short lockdown periods seems unlikely, as agricultural practices, the primary source of NH₃ emissions, remained largely unchanged during the lockdowns. This suggests that the observed rise may be more attributable to changes in atmospheric chemistry or to the impact of meteorology on NH₃ volatilization and to the reduction of other species, like SO₂ and NO_x emissions, during the lockdowns (Evangeliou et al., 2025). The single species inversion system used in this study has a limitation and a source of uncertainty to explain this rise in NH₃ emissions. These changes require studying the atmospheric chemistry of ammonia in response to variations in NO_x and SO₂ levels in the atmosphere. A combined multi-species inversion of NO_x, SO₂, and NH₃ emissions would offer valuable insights into the complex chemical interactions among these air pollutant species in the atmosphere.

There are several uncertainties and limitations associated with our global daily (at 10 d scale) inversion of the anthropogenic NH₃ emissions using IASI NH₃ observations. Although our estimates are mostly consistent and within the range of other recent inversion emissions, our inversion approach and estimates are subject to several uncertainties and limitations. The inversion approach is directly impacted by the errors associated with the observations from the satellite NH₃ retrievals and from model simulations, and it does not provide the uncertainty in emission estimates. A few studies (Cooper et al., 2017; Koukouli et al., 2018) provided some information about the uncertainties in their estimates of other short-lived species like NO_x or SO₂ using the basic or FDMB inversion approach, propagating the observation errors. Although their estimates of uncertainties do not provide the full uncertainty budget, as they do not account for uncertainties associated with model errors or the specific modeling approach, implementing a similar approach could be considered in the future to provide some indication of the uncertainties in our inversion estimates. Systematic errors in satellite retrievals, particularly notable at higher latitudes and during wintertime, may introduce inconsistencies or lead to an overestimation of emissions. Statistical inverse modeling methods (Cao et al., 2020, 2022) account for retrieval errors, but this work is generally focused on the random local and instant noise on the retrievals, and these methods are also highly impacted by systematic errors (Cao et al., 2020, 2022).

The FDMB inversion approach employs a linear sensitivity function based on the perturbations of NH₃ emissions in LMDZ-INCA model simulations, which may oversimplify the complex chemical interactions between air pollutants, including NH₃, in the atmosphere. However, in order to test the impact on the inversion results of the selection of the level of perturbations, we have also conducted a sensitivity analysis with a LMDZ-INCA model simulation using a smaller 20 % perturbation to the prior CEDS anthropogenic NH₃ emissions for the year 2019, in contrast to the original 40 % perturbation used in our FDMB inversion setup. The results show that the differences in the resulting budget of the estimated NH₃ emissions over 2019 and the globe with the application of the FDMB based on these two levels of perturbations are less than 2 %, indicating that the inversion results are not highly sensitive to the choice of perturbation magnitude within this range. As β is the only variable that changes when changing the level of perturbation, this less than 2 % change in the emission estimates necessarily stems from the changes in β due to the reduced prior NH₃ emission perturbations. The good fit between the model simulations with the inverted NH₃ emissions and the IASI NH₃ observations (Sect. 3.2) further strengthens the confidence in the linearization of the inversion problem based on 40 % perturbations to the prior estimate of the emissions. This sensitivity behavior is similar to that of previous applications of the FDMB method to the inversions of anthropogenic NO_x emissions, where different perturbation levels (e.g., 5 %–50 %) to the prior emissions resulted in minimal changes in the posterior anthropogenic NO_x emission estimates at global and regional scales (Cooper et al., 2017; Lamsal et al., 2011; Zheng et al., 2020). The use of a 40 % perturbation in our NH₃ study was motivated by the relatively high uncertainty in the current NH₃ emission inventories, particularly over regions with strong agricultural sources. Nevertheless, our sensitivity test indicates that this choice (at least within a range of 20 %–40 %) is not a critical parameter of our inversions.

Due to the sparseness of daily satellite observations of NH₃ total columns, when the number of high-quality observations within a grid cell is limited, it amplifies uncertainty in the averaged gridded dataset used in the inversions. Consequently, this may lead to an increase in uncertainty in the estimates of daily (at 10 d scale) emissions. As we focus on the inversion of dominated anthropogenic NH₃ emissions, exclusion of the emissions from other sectors like natural sources is a big challenge. This complexity is particularly pronounced in regions dominated by biomass burning NH₃ emissions from wildfires. The local mass-balance inversion approach does not incorporate the transport of ammonia from the non-local biomass burning emissions regions to the local anthropogenic grids, which may lead to an overestimation of the anthropogenic NH₃ emissions in some regions like South America, North America, and Africa. Furthermore, the conservative gap-filling approach employed in this study may introduce some biases and contribute to uncertainties in the final emission estimates.

Although the local finite difference mass-balance approach applied for the inversion of short-lived species like NH₃ in this study, which has a typical short atmospheric lifetime of a few hours to a day, is suitable for inversions at a coarse resolution (∼2°) (Cooper et al., 2017), the typical length scale of our model's spatial resolution (1.27° × 2.5°) can often be reached by the advection of NH₃ within its lifetime. The transport to neighboring grids can lead to a spatial “smearing” effect, where emissions are dispersed away from their source grid cell, introducing errors in mass-balance inversion approaches (Cooper et al., 2017; Li et al., 2019). This problem of spatial smearing in mass-balance inversion approaches is well-documented for short-lived species like NO_x or NH₃ (Cooper et al., 2017; Li et al., 2019). Such smearing can lead, on average, to the underestimation of the regional-scale emissions, as the approach overlooks the fact that the amplitude of the NH₃ signal associated with a given area source decreases with the advection downwind (Cooper et al., 2017; Li et al., 2019). For short-lived species like NO_x, some approaches such as smoothing kernels or iterative FDMB inversion approaches have been used to reduce these errors, but the latter is computationally intensive, especially for global inversions. An iterative FDMB approach (Cooper et al., 2017; Li et al., 2019) can be explored in the future to provide better accuracy in the estimates of NH₃ emissions at a feasible computational cost to overcome this limitation.

In our LMDZ-INCA model setup and inversion framework, the CEDS inventory emissions are regridded to match the model resolution. While this inevitably misses some fine-scale features, our study focuses on the broader regional patterns of NH₃ emissions rather than point-source inversions. The inversions at higher resolution, based on high-resolution regional inventories (e.g., MEIC, NEI, and CAMS-REG) and high-resolution chemistry transport model simulations can bring more robust information of the more localized NH₃ sources such as point sources at sub-national scales. However, the above-mentioned limitation, i.e., the spatial smearing effect (ignoring the advection across the chemistry transport model grid cells) of the FDMB inversion approach, would be exacerbated at such a higher resolution. Even if an iterative FDMB approach is used to overcome this smearing effect at finer resolutions, errors in the derived emission estimates can be amplified (Li et al., 2019). Therefore, application of such an inversion approach at the finer resolution may have limitations in accurately estimating the NH₃ emissions.

Note that an inverse modeling framework including observations of the full reduced nitrogen family (NHx=NH3+NH4+) and relying on tests of sensitivities of NH₃ and NH4+ to changes in NH₃ emissions could provide a more comprehensive constraint on NH₃ emissions, given the rapid gas-particle partitioning of NH₃ to NH4+ under typical atmospheric conditions. However, current satellite retrievals such as those from IASI and CrIS are primarily focused on gaseous NH₃. The current spaceborne instruments have a limited capability to detect particulate-phase NH4+. As a result, the observational constraints in our inversion framework are based only on NH₃ columns. Nevertheless, the LMDZ-INCA aerosols–chemistry transport model used in our inversion framework fully represents these chemical conversions of NH₃ to NH4+ and the partitioning and deposition processes affecting the entire NH_x family. Therefore, the LMDZ-INCA model and, implicitly, our inversion framework account for the fate of NH₃ through its interaction with NH4+ when deriving relationships between the NH₃ emissions and concentrations.

Over some regions like China and India, the rapid changes in SO₂ emissions in recent years impact the NH₃ concentration in the atmosphere significantly and thus emissions (Luo et al., 2022). Similarly, changes in NO_x emissions and concentration in the atmosphere across different regions alter the formation of ammonium nitrate from ambient ammonia. Therefore, we will investigate the potential of simultaneously assimilating NH₃, SO₂, and NO_x satellite observations to constrain the NH₃ emissions in future studies.