IASI (Infrared Atmospheric Sounding Interferometer) is a Fourier transform spectrometer that operates in the thermal infrared spectral range. It is on board the MetOp-A, MetOp-B, and MetOp-C satellites, a series of European polar-orbiting meteorological satellites managed by the European Space Agency (ESA) and the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT). The MetOp-A satellite, equipped with IASI, was launched in 2008, followed by MetOp-B and MetOp-C in 2012 and 2018, respectively. The IASI instruments operate at an altitude of 817 km in a sun-synchronous orbit with an inclination of 98.7°. Each instrument conducts measurements over a ground swath width of 2200 km, with 30 fields of view (15 on each side of the nadir). Each field of view consists of four pixels, each with a nadir diameter of 12 km. This observational strategy enables each IASI instrument to make two passes over every point on Earth daily, around 09:30 and 21:30 local time .

The assimilated observations for estimating the NH₃ emissions were the monthly IASI column concentration means over the 0.5° × 0.625° GEOS-Chem grid cell. These values were derived from the latest ANNI-NH₃-v4R-ERA5 product. Despite improvements in NH₃ column retrievals from satellite observations, there remains substantial variability in measurement uncertainty, ranging from 5 % to over 1000 % . Data selection was performed by excluding nighttime observations, irrational values (<0), and using only data with a cloud fraction <0.1 and skin temperature >263 K during the calculation of the monthly mean. While negative values are not necessarily incorrect, they are considered unrealistic in the context of NH₃ concentrations. To improve the quality of the monthly average, we removed those negative values. Additionally, we re-compared the cases of excluding negative NH₃ total column values and retaining them. As shown in Fig. S1 in the Supplement, the positive bias on the final concentrations within our study region is minimal. It is also important to note that we used daily observations from three satellites, each with a pixel resolution of approximately 12 km × 12 km, which provided us with sufficient observations to calculate the monthly average. We applied a selection criterion, using only grid averages that contain a minimum of 80 observations. This approach ensures that the grid-averaged values are statistically representative and that the monthly mean is of high quality. Notably, the time coverage of the available version 4 IASI product used was limited: MetOp-A provided data for the entire year of 2019, MetOp-B provided data from January to July 2019, and MetOp-C did not have data for 2019. Therefore, only the data from MetOp-A and MetOp-B within the 2019 time frame were used in this study. The use of both MetOp-A and MetOp-B data for 2019 ensures data continuity and enhances the reliability of the measurements. While a single satellite could provide sufficient data, using both platforms could improve temporal and spatial coverage, resulting in more accurate and robust results. To ensure robustness, we also made a brief comparison of the NH₃ column concentrations obtained from both MetOp-A and MetOp-B satellites, as shown in Fig. S2. Despite some small differences, the data from both satellites are generally consistent in terms of spatial patterns and concentration levels. Additionally, the data from the two satellites can complement each other, indicating good reliability of the results across both platforms. To further improve the data quality and ensure consistency, we performed monthly and grid averaging of the observations. This approach not only allows for a fair comparison between the observed and modeled NH₃ concentrations but also reduces the computational cost of the assimilation process. Using individual observations without averaging would result in an excessively large observational vector, which would significantly increase the computational burden. For example, without averaging, the size of the observational vector could reach 1 000 000, while with monthly and grid averaging, it is reduced to a manageable size of around 1000. This reduction in size helps to optimize the data assimilation process while maintaining the integrity of the emission estimates.

Compared to the previous version, one highlight of the latest version 4 product is that it includes averaging kernel information. The benefit of using the averaging kernel is that it can consider the vertical distribution characteristics of satellite observations, helping to correct the satellite retrieval results and making them more representative of the true distribution of the target gas or variable in the atmosphere . The impact of averaging kernels (AVKs) is supposed to be considered in the data processing. The sensitivity of IASI NH₃ observations varies with altitude, and AVKs enable the adjustment of simulated or observed NH₃ concentrations to align with the vertical distribution detected by IASI. This adjustment is particularly important for data comparison and validation against the model simulations . The formula for calculating the column concentration, after accounting for the averaging kernels, in this paper follows:

1X^m=X^a-B∑zAzamz+B. Here, X^m represents the IASI column concentration retrieved with the model profile. X^a denotes the initial IASI column concentration, with the background concentration B. The Aza values are the AVK for each vertical layer, with the model profile mz. More detailed information and the corresponding equations are provided in the Supplement, Eqs. (S8) and (S9).

The uncertainty assigned to the IASI measurements is also essential. When calculating the uncertainty of gridded monthly average NH₃ measurements, both instrumental errors σinstrumental and the representation error σrepresentation are considered. The gridded average uncertainty derived directly from IASI products was designated as the instrumental error σinstrumental, while the standard deviation of the observed samples for the gridded average was characterized as the representation error σrepresentation. The total uncertainty σintegrated for weighting the potential spread of the assimilated IASI NH₃ measurements is finally expressed as: 2σintegrated=σinstrument2+σrepresenting20.5. Four snapshots of the assimilated monthly IASI NH₃ column concentration observations and their uncertainty in January, April, July, and November can be found in Figs. a and S3. These four scenarios are selected to highlight the typical seasonal profile of the NH₃ loading over South Asia.

The Cross-track Infrared Sounder (CrIS) NH₃ column concentration and ground-based observations of NH₃ and PM_2.5 from the Central Pollution Control Board (CPCB) of India were also collected to validate our assimilation results.

The CrIS instrument was launched in 2011 on the Suomi National Polar-Orbiting Partnership (SNPP) satellite and in 2017 on the NOAA-20 satellite. The retrieval products from SNPP began in 2011 and ended in May 2021, with a data gap from April to August 2019. The NH₃ retrieval products from NOAA-20 started in March 2019. Therefore, we used retrieval products from both SNPP and NOAA-20 as independent observations for 2019. We utilized the Level 2 CrIS product from the CFPR 1.6.4 version. Specifically, only the CrIS observations during daytime, under cloud-free conditions, and with a quality flag ≥3 were selected. These original data were subsequently interpolated to achieve a spatial resolution of 0.5° × 0.625°, which is consistent with our NH₃ simulation. Similarly, we also considered the impact of the averaging kernels (AVKs) and applied the AVKs to the satellite profile data. We converted the logarithmic averaging kernels into linearized averaging kernels based on the method proposed by .

Ground observations of NH₃ in South Asia are mainly provided by the Central Pollution Control Board (CPCB, https://cpcb.nic.in/, last access: 21 October 2024), which is the official portal of the Government of India. NH₃ is measured by the chemiluminescence method as NO_x following the oxidation of NH₃ to NO_x. In that approach, NH₃ is determined from the difference between the NO_x concentration with and without the inclusion of NH₃ oxidation . The ground-level NH₃ concentration data from CPCB were successfully collected. There were NH₃ surface concentration observations from 33 stations available in 2019; the distribution of these stations is shown in Fig. .

PM_2.5 observations from CPCB were also used in the assimilation validation. The PM_2.5 observations were selected before they were used, which follows : First, select the hourly PM_2.5 data greater than PM₁₀. Then, filter out the hourly PM_2.5 data that fall outside the range of day_mean - 3 × standard deviation and day_mean + 3 × standard deviation. Additionally, ensure that each day contains at least 20 h of data. Finally, process the data into monthly averages for subsequent validation. The distribution of the ground stations where the PM_2.5 values were used in this paper can be found in Fig. , and detailed information about the stations is provided in Tables S1–S3 in the Supplement.

This study employs the four-dimensional ensemble variational (4DEnVar) data assimilation-based NH₃ emission inversion system that was developed by . The general idea of assimilation-based emission inversion is to find the most likely estimate, which in this case is the monthly NH₃ emission field, given the prior NH₃ emissions and the observations. The calculation is conducted through minimizing the cost function J: 3J(f)=12f-fbTB-1f-fb+12{y-HM(f)}TO-1{y-HM(f)}. Here, f denotes the vector of the NH₃ estimated emission field, with its units typically expressed in kg m⁻² s⁻¹. Additionally, fb denotes the prior monthly NH₃ emission vector from CEDS, as will be described in Sect. . B represents the background error covariance matrix associated with the prior emission estimate. Here, we assume that the uncertainty in the NH₃ emission can be compensated by a spatially varying tuning factor α. The α values are defined to be random variables with a mean of 1.0 and a standard deviation σ=0.2. In addition, a correlation matrix C is introduced for quantifying the spatial correlation between two α values in the grid i and j as: 4C(i,j)=e-(di,j/l)2/2, where di,j represents the distance between two grid cells i and j. l here denotes the correlation length scale, which controls the spatial degrees of freedom of the α values. An empirical parameter l=300 km, which is used in the NH₃ emission inversion in China , is also used in this study. With the spatial correlation matrix and the emission uncertainty, the background error covariance matrix could then be constructed as: 5B(i,j)=σ2⋅fb(i)⋅fb(j)⋅C(i,j).

M here represents the GEOS-Chem model (as will be illustrated in Sect. ) driven by the emission f. H is the observational operator that transfers the simulated NH₃ 3D concentration result into the observational space. y represents the monthly IASI NH₃ column concentration observations, while O is the observation error covariance matrix. Here, we assume the IASI observation representation errors are independent from each other. O therefore is a diagonal matrix filled with the square of the integrated uncertainty, as described in Sect. . Meanwhile, a minimum measurement error is used to prevent the posterior from being too close to low-value observations, thereby avoiding model divergence: 6Oi,i=min⁡1.0×1016molec cm-2,σintegrated2.

More information about how we minimize the cost function Eq. () can be found in .

GEOS-Chem, a three-dimensional (3-D) global tropospheric chemistry model, is driven by assimilated meteorological data obtained from the Goddard Earth Observing System (GEOS) at the NASA Data Assimilation Office (DAO) . GEOS-Chem incorporates a fully integrated chemistry system involving aerosol, ozone, NO_x, and hydrocarbons, as described by . The wet deposition scheme is explained by for water-soluble aerosols and by for gaseous components. Dry deposition is modeled using the resistance-in-series scheme proposed by , as applied by . Size-specific aerosol dry deposition follows the approach outlined by .

A nested grid simulation within the GEOS-Chem model v13.4.1 is conducted to simulate the atmospheric environment over South Asia. The nested domain (60–98° E, 4–40° N), shown in Fig. , has a horizontal resolution of 0.5° latitude by 0.625° longitude, accompanied by 47 vertical layers. The model is driven by meteorological fields from the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) reanalysis dataset provided by the Global Modeling and Assimilation Office (GMAO) at NASA. The model employs a 3 month spin-up period to minimize the influence of the initial conditions. Lateral boundary conditions for the nested domain are updated every 3 h using output from the global GEOS-Chem simulation at 2° × 2.5° resolution. Chemical initial conditions are also obtained from the global simulation to ensure consistency.

The NH₃ emissions inventory employed to drive GEOS-Chem originated from the Community Emissions Data System (CEDS, https://doi.org/10.25584/PNNLDH/1854347, ) inventory, which has been widely used for modeling the South Asia atmospheric pollutants, e.g., VOCs and PM_2.5 pollution . The CEDS inventory includes various sources encompassing agricultural, energy production, industrial, residential, and commercial activities, ships, solvent use, surface transportation, and waste processing . The bulk of NH₃ emissions originate from agricultural practices. Specifically, these emissions stem predominantly from farmlands, including crops such as wheat, maize, and rice, as well as manure from livestock, including cattle, chicken, goats, and pigs . The CEDS emission estimates were coarse-grained into the model resolution 0.5° × 0.625° before being utilized to drive the GEOS-Chem simulations. Examples of the CEDS emission over South Asia are presented in Fig. , which plots the total NH₃ emission fluxes for January, April, July, and November of the year 2019. Additionally, the model's biogenic emissions are based on the MEGAN2.1 (Model of Emissions of Gases and Aerosols from Nature) inventory , while the biomass burning sources driving the model are based on the GFEDv4 (Version 4 of the Global Fire Emissions Database) inventory . The use of IASI and CrIS observations, along with GEOS-Chem simulations, is outlined in Table 1.

We first present the spatial distribution of NH₃ column concentrations from satellite observations and model results driven by either the prior or posterior inventories. Then, we examine their seasonal variation in 2019 and the long-term trends from 2015 to 2023.

By assimilating IASI NH₃ column concentrations, the posterior anthropogenic monthly NH₃ emission inventories for 2019 were updated. Scenarios of the posterior emission inventories, along with the increments (posterior minus prior), for January, April, July, and November are shown in Fig. b–c. The prior, posterior, and increment data for the remaining months of 2019 are provided in Figs. S7–S9 in the Supplement. Our posterior inventory demonstrated that, in general, the primary sources of NH₃ originated from North India, Pakistan, and Bengal. This finding is consistent with the CEDS inventory, as well as with other studies . However, a huge discrepancy emerged when we compared the posterior and prior results, particular for April (in Fig. b) and July (in Fig. S3c). The posterior results reveal a distinct seasonal emission profile compared to the prior. Specifically, emissions during spring are significantly overestimated by the prior model, whereas summer emissions are underestimated by up to 3-fold.

To better illustrate the differences in timing profiles throughout the year, the monthly average emission intensity over South Asia was calculated and is shown in Fig. b. The prior anthropogenic emission inventory exhibits a “double-peak” pattern, mirroring the profile of the average NH₃ concentration displayed in Fig. a. The emission flux reaches its maximum in May, peaking at approximately 0.6 g m⁻², with a secondary peak occurring in September around 0.25 g m⁻². In contrast, the assimilation that integrates prior CEDS emissions with IASI measurements shows much lower intensities from January to May, with the largest negative differences (>0.3 g m⁻²) observed in May. While the prior emissions remain relatively low during the summer, the emission inversion reveals positive increments, with the posterior inventory indicating the maximum emission flux in July, peaking at approximately 0.4 g m⁻². In general, the posterior emissions also display a “double-peak” pattern; however, the peaks occur in May and July, in contrast to the May and September peaks observed in the prior emissions.

The substantial emissions in July, as indicated by the posterior anthropogenic inventory, can be attributed to the increased fertilizer application for crops during the summer season . As shown in Table 2, the sowing period for crops in South Asia is generally from May to July, with July being the peak growth period for crops, resulting in a large amount of fertilization, resulting in July surpassing May in emission intensity. From July to September, as rice and other crops progress through their growth stages, fertilizer application typically decreases, leading to a gradual reduction in NH₃ emissions. Additionally, temperatures decline from August to September Fig. S6b, reducing the volatilization rate of NH₃, thereby leading to a further decrease in emissions. This pattern occurs because NH₃ volatilization is strongly influenced by temperature .

The convergence of prior and posterior anthropogenic emission intensities in June is attributed to the overall offsetting of negative and positive increments in the region, as shown in Fig. S9f. As depicted in panel (c) of Fig. , the negative increments observed in January and April primarily originate from the Indian region, while the positive increments in July and September are predominantly observed in the same area. Additionally, the posterior emission estimates, which are based on CrIS, have now been included.

To evaluate our inversion results, we compared the atmospheric NH₃ simulation driven by either the posterior emission (referred to as the posterior simulation) or the prior one against the observations, including the assimilated IASI column data and the independent CrIS retrieval and ground-based NH₃ and PM_2.5 concentration measurements.