An accurate radiative transfer (RT) model is an important component in the inversion system for simulating upwelling thermal radiation that would be observed by FY-4B/GIIRS when given the relevant atmospheric, surface, and instrumental parameters as inputs. The upwelling spectral radiance is computed following the radiative transfer theory for thermal radiation that has been described in Clough et al. (2006) and Hurtmans et al. (2012). Under clear-sky conditions, scattering by clouds and aerosols can be ignored. The upwelling radiance received by FY-4B/GIIRS can be accurately approximated by the sum of four main components, including the upwelling surface emission, the upwelling atmospheric emission integrated from the bottom to the top of the atmosphere, the surface-reflected downwelling atmospheric emission, and the surface-reflected solar radiation. Although the last component is very small in the longwave band, it is added here for completeness. The absorption microwindow (955–975 cm-1) used for retrieval is shown in Fig. 2a. The microwindow contains strong NH3 absorption features that are distinguishable from important interference gases (CO2, O3 and H2O) in the absorption window, as demonstrated in Fig. 2 from a sensitivity experiment that compares absorptions of NH3 and perturbed interference gases.

The atmospheric, surface, and instrumental parameters used to drive the forward model are adopted from various sources. These parameters are the atmospheric state such as the profiles of temperature, water vapor, and atmospheric composition; the surface parameters such as the surface emissivity; and the instrumental specifications such as instrument spectral response function and observing geometries. Specifically, the atmospheric temperature, H2O, and O3 data are extracted from European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5) data (Hersbach et al., 2020), and CO2 is extracted from ECMWF Copernicus Atmosphere Monitoring Service (CAMS) global inversion-optimized greenhouse gas fluxes and concentrations (ECMWF, 2022). For the surface land data, we used the global infrared land surface emissivity database from the University of Wisconsin-Madison (UOW-M) (Seemann et al., 2008). The emissivity values at 925 and 1075 cm-1 are used to estimate the a priori emissivity for the retrieval microwindow. Two factors (slope and curvature) are used in the state vector to scale the wavelength-dependent emissivity values; surface skin temperature and surface pressure are extracted from ERA5 hourly data on a single level (Hersbach et al., 2020). The absorption coefficient lookup tables for calculating gas absorption are built using the extensively validated Line-By-Line Radiative Transfer Model (LBLRTM v12.11; Clough et al., 2005).

Since the NH3 is short-lived and highly concentrated in the PBL, we therefore only retrieve the layers below 200 hPa. The forward model uses fixed vertical grids with equally separated layers with similar thickness (about 1 km for layers below 200 hPa and about 5 km for layers above), which is close to the grid settings in Hurtmans et al. (2012) and Clough et al. (2005). The thickness of the bottom layer is variable and determined by the surface pressure of a specific location. The number of layers below 200 hPa ranges from 7 (for high-altitude regions such as the Tibet Plateau) to 11 layers (for low-altitude regions such as the ocean).

The goal of the retrieval algorithm for retrieving NH3 from FY-4B/GIIRS based on optimal estimation theory is to find a solution for the state vector, which consists of NH3 profile and auxiliary parameters, such that the simulated spectra from the RT forward model best fit the measured spectra. The auxiliary parameters include the H2O profile, scale factors for the columns of the remaining interference gases, the surface skin temperature, and scale factors for the atmospheric temperature profile. The solution from the retrieval algorithm is the state vector which minimizes the spectral fitting error. The Levenberg–Marquardt modification of the Gauss–Newton method is used to search the solution. The optimal estimation method has been described thoroughly in Rodgers (2000) and applied in several previous studies by the group (Zeng et al., 2017, 2021; Natraj et al., 2022; Zeng et al., 2023). The parameters in the state vector to be retrieved from the algorithm are listed in Table 1. Vertical profiles of NH3 and H2O are retrieved, while for minor interference gases, total columns are retrieved by scaling an a priori profile. Other parameters to be retrieved include the surface skin temperature, a scaling factor for the atmospheric temperature profile, and the slope and curve for the surface emissivity. We only retrieve the layers below 200 hPa and use the a priori profile for layers above to compute total columns.

Two important metrics from the optical estimation method for interpreting the retrieval results are the DOFS and averaging kernel (AK) matrix. The AK matrix is a metric that quantifies the sensitivity of the retrieval to the true state by the observing system. The full AK matrix (m×m) is given by 1A=KTSε-1K+Sa-1-1KTSε-1K, where each element Aij of A represents the derivative of the NH3 retrieval at level i with respect to the NH3 truth at level j. The matrix dimension m is the number of atmospheric layers; K is the Jacobian matrix, which is the first derivative of the forward model with respect to the state vector; Sa is the a priori covariance matrix for the state vector; and Sε is the measurement error covariance matrix, which is assumed to be a diagonal matrix constructed using the spectra noise estimates. Note that similar to the CO retrieval algorithm (Zeng et al., 2023), we have enlarged the spectra noise by a factor of 2.0 such that the averaged reduced χ2 value from the optimal estimation NH3 retrieval is close to 1.0. This extra noise represents the unaccounted uncertainty from the forward model and absorption spectroscopy by the original instrument noise alone.

A “perfect” observing system, which has sufficiently good sensitivity to each element in the retrieval vector, would have an AK matrix close to an identity matrix by theory. In reality, the detectivity is limited by various factors including the spectral noise, a priori uncertainty, and the sensitivity of the spectra to the geophysical variables in the state vector. As a result, the AK can be very different from an identity matrix. In general, the information from the true state is smoothed vertically over different layers by the retrieval algorithm. In this case, the rows of AK represent the smoothing functions. As described in Rodgers (2000), the trace of the AK matrix is defined as the DOFS, which represents the number of independent elements of information extracted from the spectra by the retrieval algorithm for constraining NH3. The DOFS is an important metric that quantifies the vertical resolution of the retrieval profile. For example, a DOFS of 1.0 means that, given the assumed Sa, at least one independent piece of information can be retrieved from the spectral measurement to constrain the vertical distribution of NH3. Note that the DOFS is highly dependent on the magnitude of the assume Sa, an indicator of the a priori knowledge. If Sa characterizes a weaker constraint, indicating less a priori knowledge, the DOFS will be higher as relatively more information will be taken from the measurement.

A fixed a priori profile is preferred for the purpose of this study for two reasons: (1) a fixed a priori profile eases the interpretation of the results compared to a time-varying a priori profile. Any changes seen in the spatial and temporal patterns in NH3 relative to the a priori profile reflect the information gained from the FY-4B/GIIRS spectra. (2) It is not applicable to get a reasonable a priori estimate for all hours in a day from just the spectra (e.g., using channel brightness temperature difference as in Shephard et al., 2011, and Warner et al., 2016) without relying on model simulations because the diurnal change of TC that affects geostationary (GEO) satellite observation is much more complex than that in the two overpasses for LEO satellite each day. The single a priori NH3 profile, as shown in Fig. 3a, for all retrievals in the retrieval algorithm is derived from NH3 simulations from the Goddard Earth Observing System composition forecast (GEOS-CF; Keller et al., 2021) model developed by NASA's Global Modeling and Assimilation Office (GMAO). A year of simulation in 2022 is used to get the mean and standard deviation of NH3 vertical distribution. To avoid oversampling of the background regions, only simulations in the representative land regions in East Asia (20–60∘ N, 110–120∘ E) and South Asia (20–40∘ N, 70–100∘ E) are used. The negative value toward the lower end of the error bar does not have physical meaning; it is caused by the large standard deviation derived from model simulations that do not strictly follow a normal distribution. The a priori total NH3 column is about 1.5×1016 molec. cm-2. To construct the correlation matrix, we used a correlation length of 3 km based on our analysis of the GEOS-CF reanalysis. Most of the layers show correlation lengths between 1 to 3 km, and we use an upper bound (3 km) to increase the stability of the retrieval system. The covariance matrix calculated based on the a priori error and the correlation matrix is shown in Fig. 3b.

After cloud screening, there are 11.7 million clear-sky data points in total for the 6 months from July to December 2022. In the post-processing, multiple filters are applied to ensure good retrieval quality. First, retrievals that fail to converge after 10 iterations are excluded. Second, retrievals with a goodness of fit, quantified by reduced χ2, of less than 1.5 are excluded. Lastly, retrievals with a RMSE of the fitting residual larger than 0.25 K are excluded. After post-filtering, about 10.5 million data points pass the filters. The histograms of the reduced χ2 and spectral fitting residual are shown in Fig. S1 in the Supplement (after filtering) and Fig. S2 (before filtering). The average reduced χ2 after post-filtering is 0.76, suggesting a satisfactory goodness of fit. In the following analysis, an extra filter based on DOFS may apply to exclude data with low DOFS and, therefore, low information content extracted from the observed spectra.

A synthetic experiment is carried out by (1) generating simulated synthetic spectra based on pre-determined NH3 profiles which can be regarded as the “truth”, (2) adding assumed noise according to the spectra noise of FY-4B/GIIRS, and (3) applying the FY-GeoAIR algorithm to retrieve NH3. By comparing the retrieval to the “truth”, we can evaluate the performance of the retrieval algorithm and its relationship with relevant driving factors. In this experiment, the “truth” NH3 profiles are extracted from the GEOS-CF model simulations on 6 representative days: 7 July, 5 August, 6 September, 10 October, 15 November, and 18 December 2022, when the available number of clear-sky observations is among the largest in the specific month. By randomly sampling 500 data points for each observation cycle from the FY-4B/GIIRS clear-sky observations, we carried out 36 000 simulations in total. The retrieved NH3 columns are finally compared with the “truth” and correlated with the DOFS, as shown in Fig. 4. Simulations with a DOFS less than 0.3 are not shown due to their high uncertainty and low information content extracted from the spectra measurement. The scatter plot suggests that the consistency between the retrieval and the “truth” increases when the DOFS becomes larger. For retrievals with a low DOFS, the retrieval values are close to the a priori value, which is about 1.5×1016 molec. cm-2. For the several outliers that have a high DOFS but with poor retrieval, it is likely because the “truth” NH3 profile structure is far away from the a priori profile structure. For a DOFS >0.5, the RMSE of the retrieval is about 1.67×1016 molec. cm-2, while for DOFS >0.7, the RMSE reduces to 1.37×1016 molec. cm-2, representing error for a single retrieval. Since the retrieved NH3 columns have a monthly mean between 2.0×1016 and 6.0×1016 molec. cm-2 (as shown in Sect. 4.2), this synthetic experiment results indicate that the retrieval error is on average between 23 % and 68 % for a single retrieval when the DOFS >0.7. On the other hand, when an ensemble mean (e.g., monthly mean) of NH3 columns is derived, the resulting error for the mean can be much smaller (reduced by a factor of (N), where N is the number of observations) when a large number of observations is available.

In addition, two more experiments have been carried out to (1) compare the difference in retrievals from a different microwindow (920–940 cm-1) to investigate the possible impact of spectral noise and (2) investigate the impact of the a priori NH3 vertical shape on the retrievals. The details are described in Sects. S1 and S2 in the Supplement, respectively. The results show that the DOFS values show high consistencies, with a correlation coefficient of 0.97, suggesting the two microwindows contain similar information in capturing the NH3 variabilities. The correlation coefficient between the two retrieved NH3 column datasets is 0.81, with a root mean square error of 3.2×1015 molec. cm-2, suggesting the spectral noise is not causing large bias. The results show that the mean and standard deviation of the fractional error are 1.0 % and 9.65 %, respectively, for the reduced PBL excess profile, and 0.9 % and 7.6 %, respectively, for the enhanced PBL excess profile. Fortunately, there is no large systematic bias, and the averaged error is within 10 % in our cases where profiles differ by a factor of 2.

This section conducted information content analysis by investigating the spatial and diurnal changes of DOFS from NH3 retrievals and how the DOFS changes are related to TC. In addition, we examine the diurnal changes of the vertical sensitivity as quantified by AK matrix. In particular, we focus on three representative regions including source regions in the North China Plain, North India, and a background region in Mongolia.

The spatial maps of DOFS, as shown in Fig. 5, for different times in a day clearly show the spatial gradient and diurnal change. In July and October, the DOFS values in the afternoon are usually the highest and those in the evening the lowest. In December, nighttime DOFS are significantly higher than other seasons. Previous studies by Clarisse et al. (2010, 2021) and Bauduin et al. (2017) using IASI observations have shown that the DOFS is primarily driven by the TC. When thermal contrast is close to zero, measurement sensitivity is low, and the DOFS values are close to zero. Large positive TC increases sensitivity and results in NH3 spectral signatures that are seen in absorption. Large negative TC also allows for sensitive measurements, this time allowing NH3 spectral signatures to be seen in emission. Negative TC corresponds to the situation where the atmosphere is warmer than the surface, allowing to decorrelate the surface layer with the rest of the lower troposphere. In addition, higher concentration of target gases provides stronger detectivity than lower concentration. The relationships between TC and the DOFS are illustrated in Fig. 6 for the three representative regions, including (1) the North China Plain, which represents industrialized and agricultural regions with persistently high NH3 emissions; (2) North India, which represents another important NH3 source region in Asia; and (3) Mongolia, which represents a NH3 background region. A typical “butterfly” shape can be seen in almost all cases, except for North India in July when there are much fewer observations due to clouds. In general, the DOFS increases when the TC becomes either more positive or more negative, consistent with results from Clarisse et al. (2010) and Bauduin et al. (2017) based on polar-orbiting satellites. In NH3 source regions (e.g., the North China Plain and North India), the DOFS values are higher for the same TC compared with non-source region (e.g., Mongolia), suggesting the contribution from higher NH3 concentration to the total information content.

This strong correlation between DOFS and TC or NH3 abundance is also reflected in the spatial maps of DOFS values in Fig. 5 when analyzed with the corresponding TC maps in Fig. S2. The source regions in the North China Plain and North India have higher DOFS values than other non-source regions, such as the Tibetan Plateau, although it has large TC. For the same region (e.g., the North China Plain), the higher DOFS is driven by the more positive TC in the afternoon in July, while at nighttime the TC is closer to zero, which leads to a much lower DOFS. As it approaches the winter season, from October to December, the diurnal cycle of TC, which shifts from positive in the daytime to negative in the nighttime, gradually become stronger. The changes are basically driven by the faster warming or cooling properties of the land compared to the atmosphere. Fortunately, both situations favor the detection of NH3 using thermal infrared and lead to the high DOFS values in both the daytime and nighttime in both October and December.

As mentioned above, measurement sensitivity of NH3 is driven by TC and the NH3 abundance (Clarisse et al., 2010). This is also illustrated in the Appendix Fig. A1a and b for a large positive and negative TC. As described above, while a positive TC leads to stronger absorption features, a negative TC causes spectral emission features, allowing the detection of NH3 also during the night (see also the example GIIRS spectra shown in Clarisse et al., 2021). In both cases we see that the averaging kernels peak at the surface, and the posteriori uncertainty in the retrievals of the surface layer are largely reduced compared to the a priori uncertainties. However, when the TC is small, as in the Appendix Fig. A1c, the DOFS values become smaller, and the AK peaks higher up in the atmosphere (in this case, in the second layer). The retrieved value remains close to the a priori value, and the posteriori error is almost the same as the a priori error, indicating low information content of the measurement. These examples illustrate the importance of TC for infrared sounding of boundary layer NH3. An important advantage of GEO compared to LEO IR sounders is that they make observations throughout the day, such that optimal measurement conditions (large TC) can be found more readily. The diel variations of TC and DOFS are illustrated in the Appendix Fig. A2 for the North China Plain and North India. LEO IR sounders like IASI with Equator crossing times at 09:30 and 21:30 LT in general do not measure at the time when measurement sensitivity (or DOFS) is largest. The optimal time is found around noon.

The short lifetime of NH3 of hours to days means that the NH3 concentration is highly concentrated in the planetary boundary layer (PBL) around the source region. This is also illustrated by the significant higher concentration below 800 hPa in the a priori NH3 profiles (Fig. 3). As a result, thermal infrared observation of NH3 has high sensitivity closer to the surface compared to relatively longer-lived air pollutant such as carbon monoxide. The vertical sensitivities of FY-GeoAIR NH3 retrievals are shown in Fig. 7 for the three representative regions using the corresponding averaging kernel diagonal vectors, which are measures of the DOFS for each vertical layer. We can see the diurnal AK values peak at the surface layer for the North China Plain for all months, especially for October and December, due to the high NH3 concentration and favorable TC changes. In July, the nighttime sensitivity is significantly reduced in the surface layers. In North India, the bottom layers' sensitivity is at its highest at midnight in October and December due to highly negative TC. In July, the TC close to zero leads to much lower AK values in North India. In Mongolia, the low background NH3 concentration means the AK values are low over all vertical layers. The small changes in DOFS are primarily driven by the diurnal change of TC in this case. Overall, the NH3 retrievals using FY-GeoAIR algorithm from FY-4B/GIIRS observations show high detectivity in the surface layer, especially for source regions in the North China Plain and North India.

Spatial distribution maps of NH3 columns are averaged for every 4 h period in a day and re-gridded into 0.5∘ × 0.5∘ for every 2 months: July–August, September–October, and November–December. Before the aggregation, the post-filtered NH3 retrievals are further screened by the criteria of DOFS >0.5. The screened NH3 retrievals from the two microwindows are further averaged for the mapping. The results are shown in Figs. 8 and 9. The data gaps, especially in the Tibet Plateau, result from data filtering due to the low DOFS. The cloud filtering has considerably impacted data availability, in particular in North India in July–August during the monsoon season. The nighttime data in summer have been mostly filtered due to their low TC and as a result low DOFS. From these maps, obvious diurnal cycle of NH3 columns can be seen from all months. The North China Plain and North India, which are two agriculturally intensive regions with irrigated crops and a high density of livestock, show the highest values over the region. As explained in Wang et al. (2020), the causes of high NH3 loading in North India are due to the weak chemical loss and weak horizontal diffusion in North India, which are slightly different from those in the North China Plain.

The general diurnal cycle of NH3 columns can be primarily explained by three possible driving factors, as concluded in the summary in Clarisse et al. (2021), including the day–night difference in agriculture activities as a major source of NH3, the temperature dependence of NH3 emissions driven by diurnal and seasonal temperature changes, and the conversion between NH3 gas and particulate driven by the day–night change of meteorological conditions. These can be used to interpret the quantitative analysis of the diurnal cycle as shown in Fig. 10 for the North China Plain and North India. The corresponding diurnal changes of TC and DOFS are shown in the Appendix Fig. A2. The day–night contrast of NH3 columns from IASI on board Metop-B is also indicated to check if the day–night gradients between IASI and GIIRS are consistent. Specifically, the more significant diurnal cycle in summer (July–August) in the North China Plain, captured by both GIIRS retrievals, can be explained by the higher temperature-related emissions from plants and soils and stronger daytime emissions from agricultural activities (Meng et al., 2018). In addition, the relatively low temperature and higher humidity in the nighttime, relative to the daytime, contribute to the conversion from NH3 to particulates, which leads to a lower NH3 concentration. In North India, unfortunately, insufficient data are available in July–August after post-filtering. In September–October and November–December, the diurnal cycles become less significant compared to the summer months as the main driving factors become less important. Interestingly, the winter diurnal cycle in the North China Plain and North India show an opposite pattern to the diurnal cycle in summer. The slight increase in NH3 columns in the nighttime, captured by both GIIRS and IASI retrievals, may be due to the shallower nocturnal boundary layer that traps the surface emissions (Tevlin et al., 2017; Clarisse et al., 2021). To ensure the diurnal change is not affected greatly by data quality, we also compare the GIIRS results using data with a DOFS larger than 0.5 and 0.7, respectively, two thresholds that are high enough to ensure the quality of the retrievals. We can see that the difference in the diurnal cycle of NH3 columns from FY-4B/GIIRS retrievals is not significant, and therefore different data filters do not affect the general patterns of NH3 diurnal cycle. Note that the variability of NH3 columns within the region is large as shown by the error bars (1 standard deviation). This large variability is a result of NH3's short lifetime and the spatial heterogeneity of its emissions. Moreover, when compared with the averaged uncertainty of a single retrieval (1.37×1016 to 1.67×1016 molec. cm-2 as derived from the retrieval experiment in Sect. 3.5), the day–night contrast of the averaged diurnal variations of NH3 columns as shown in Fig. 10 may not be significant for the North China Plain in September–October and the North India in November–December.

IASI on board Metop-B measures NH3 two times a day at 09:30 and 21:30 LT (Equator crossing times), respectively, in the morning and evening. The NH3 data from IASI are retrieved based on the hyperspectral radiance index (HRI) and a trained neural network that relates the HRI to NH3 distributions (Whitburn et al., 2016). Subsequent improvements to the algorithm and data product are outlined in Van Damme et al. (2017, 2021). For the comparison, the latest version 4 (Clarisse et al., 2023) of the IASI is used, with data originating from IASI/Metop-B from July to December 2022. We filtered out the data with cloud cover larger than 20 %. Note that the a priori vertical profile of NH3 in IASI is different from the a priori profiles for the FY-4B/GIIRS retrievals. The a priori NH3 in IASI algorithm assumes a Gaussian shape, with a peak altitude set at the surface over land. The width of the Gaussian shape is equal to the boundary layer height. Two different comparisons are carried out, as follows.