Articles | Volume 21, issue 3
Atmos. Chem. Phys., 21, 2067–2082, 2021
Atmos. Chem. Phys., 21, 2067–2082, 2021

Research article 11 Feb 2021

Research article | 11 Feb 2021

High-resolution hybrid inversion of IASI ammonia columns to constrain US ammonia emissions using the CMAQ adjoint model

High-resolution hybrid inversion of IASI ammonia columns to constrain US ammonia emissions using the CMAQ adjoint model
Yilin Chen1, Huizhong Shen1, Jennifer Kaiser1,2, Yongtao Hu1, Shannon L. Capps3, Shunliu Zhao4, Amir Hakami4, Jhih-Shyang Shih5, Gertrude K. Pavur1, Matthew D. Turner6, Daven K. Henze7, Jaroslav Resler8, Athanasios Nenes9,10, Sergey L. Napelenok11, Jesse O. Bash11, Kathleen M. Fahey11, Gregory R. Carmichael12, Tianfeng Chai13, Lieven Clarisse14, Pierre-François Coheur14, Martin Van Damme14, and Armistead G. Russell1 Yilin Chen et al.
  • 1School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States
  • 2School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, GA 30332, United States
  • 3Department of Civil, Architectural, and Environmental Engineering, Drexel University, Philadelphia, PA 19104, United States
  • 4Department of Civil and Environmental Engineering, Carleton University, Ottawa, Ontario K1S5B6, Canada
  • 5Resources for the Future, Washington, D.C. 20036, USA
  • 6SAIC, Stennis Space Center, MS 39529, USA
  • 7Mechanical Engineering Department, University of Colorado, Boulder, CO 80309, USA
  • 8Institute of Computer Science of the Czech Academy of Sciences, Prague, 182 07, Czech Republic
  • 9Institute for Chemical Engineering Sciences, Foundation for Research and Technology Hellas, Patras, 26504, Greece
  • 10School of Architecture, Civil & Environmental Engineering, Ecole polytechnique fédérale de Lausanne, 1015, Lausanne, Switzerland
  • 11Atmospheric & Environmental Systems Modeling Division, U.S. EPA, Research Triangle Park, NC 27711, USA
  • 12Department of Chemical and Biochemical Engineering, University of Iowa, Iowa City, IA 52242, USA
  • 13NOAA Air Resources Laboratory (ARL), Cooperative Institute for Satellites Earth System Studies (CISESS), University of Maryland, College Park, MD 20740, USA
  • 14Université libre de Bruxelles (ULB), Spectroscopy, Quantum Chemistry and Atmospheric Remote Sensing (SQUARES), Brussels, Belgium

Correspondence: Armistead G. Russell (


Ammonia (NH3) emissions have large impacts on air quality and nitrogen deposition, influencing human health and the well-being of sensitive ecosystems. Large uncertainties exist in the “bottom-up” NH3 emission inventories due to limited source information and a historical lack of measurements, hindering the assessment of NH3-related environmental impacts. The increasing capability of satellites to measure NH3 abundance and the development of modeling tools enable us to better constrain NH3 emission estimates at high spatial resolution. In this study, we constrain the NH3 emission estimates from the widely used 2011 National Emissions Inventory (2011 NEI) in the US using Infrared Atmospheric Sounding Interferometer NH3 column density measurements (IASI-NH3) gridded at a 36 km by 36 km horizontal resolution. With a hybrid inverse modeling approach, we use the Community Multiscale Air Quality Modeling System (CMAQ) and its multiphase adjoint model to optimize NH3 emission estimates in April, July, and October. Our optimized emission estimates suggest that the total NH3 emissions are biased low by 26 % in 2011 NEI in April with overestimation in the Midwest and underestimation in the Southern States. In July and October, the estimates from NEI agree well with the optimized emission estimates, despite a low bias in hotspot regions. Evaluation of the inversion performance using independent observations shows reduced underestimation in simulated ambient NH3 concentration in all 3 months and reduced underestimation in NH4+ wet deposition in April. Implementing the optimized NH3 emission estimates improves the model performance in simulating PM2.5 concentration in the Midwest in April. The model results suggest that the estimated contribution of ammonium nitrate would be biased high in a priori NEI-based assessments. The higher emission estimates in this study also imply a higher ecological impact of nitrogen deposition originating from NH3 emissions.

1 Introduction

Ammonia (NH3) emissions play a major role in ambient aerosol formation and reactive nitrogen deposition (Stevens, 2019: Houlton et al., 2013). However, our understanding of NH3 sources and sinks is limited by the large uncertainties present in the NH3 emissions inventories (Xu et al., 2019; McQuilling and Adams, 2015). In chemical transport models, uncertainties in NH3 emissions propagate into the dynamic modeling of the atmospheric transport, chemistry, and deposition of NH3, other reactive nitrogen species, and other key atmospheric constituents associated with NH3 (Heald et al., 2012; Paulot et al., 2013; Kelly et al., 2014; Zhang et al., 2018b), hindering an accurate assessment of the various NH3-related environmental impacts and the associated sources. The large uncertainties in the NH3 emission inventories are partially due to a lack of sufficient in situ NH3 measurements that could be used to constrain emission estimates (Zhu et al., 2015).

Emerging satellite observations of gaseous NH3 provide a unique opportunity to better constrain the bottom-up NH3 emission estimates for both their spatial distribution and seasonality. Bottom-up inventories calculate the NH3 emissions based on estimated activity levels and corresponding emission factors, both of which are subject to high uncertainties, particularly for agricultural sources, the major contributor (Cooter et al., 2012; McQuilling and Adams, 2015). Several studies have utilized NH3 column density retrieved from the Infrared Atmospheric Sounding Interferometer (IASI) (Clarisse et al., 2009; Van Damme et al., 2015b) or the Atmospheric Infrared Sounder (AIRS; Warner et al., 2016) as well as the inferred surface mixing ratio of NH3 from the Cross-track Infrared Sounder (CrIS; Shephard and Cady-Pereira, 2015; Shephard et al., 2020) to characterize the spatiotemporal distribution of NH3. These satellite measurements are useful for supplementing emission inventories to identify and quantify underestimated or missing emission hotspots, especially in intensive agricultural zones (Van Damme et al., 2018; Dammers et al., 2019; Clarisse et al., 2019). These studies find that the satellite-derived emission estimates are often twice as much as the bottom-up estimates on a regional scale and can be over 10 times higher over hotspots. However, the NH3 retrievals from satellites are also subject to large uncertainties when the signal-to-noise ratio is low, which limits their ability to accurately measure NH3 columns in low-emission areas (Clarisse et al., 2010; Van Damme et al., 2015a).

Inverse-modeling-based optimization combines the information from a priori emission inventories and observations and allows us to use the information from both. As one of the inverse modeling methods, the four-dimensional variational assimilation (4D-Var) method seeks the best emission estimate by minimizing a cost function that measures the differences between observations and model predictions, as well as the differences between a prior and adjusted emission estimates. 4D-Var can be computationally expensive at fine model resolutions or with a large set of observations to be assimilated (Brasseur and Jacob, 2017). Recent studies have taken advantage of the implementation of the adjoint technique in the chemical transport models to conduct 4D-Var for optimizing emissions estimation (Zhu et al., 2013; Paulot et al., 2014; Zhang et al., 2018c). The adjoint-based inversion method calculates the gradients of a cost function analytically and searches for the solution using a steepest-descent optimization algorithm through iterating (Brasseur and Jacob, 2017). By testing the performance of the inverse modeling method using artificial observational data, Li et al. (2019) proposed that a two-step optimization process, which combines the iterative mass balance (IMB) method and the 4D-Var method, can further reduce the computational cost. The IMB method assumes a linear relationship between the NH3 column density and local NH3 emission and searches for the emission scaling factors iteratively until the simulated NH3 column density converges to the observations. At a coarse (2×2.5) resolution, the IMB method is as effective as the 4D-Var method and requires two-thirds less computational time. In the second step, emission scaling factors obtained from the IMB method with a coarser resolution are used as an initial starting point for the 4D-Var optimization process to reduce the overall computational time (Li et al., 2019).

This work utilizes satellite observations from the IASI-NH3 column density measurements (IASI-NH3) (Clarisse et al., 2009;Van Damme et al., 2017), to provide a high-resolution, optimized NH3 emission inventory for the US developed using an adjoint inverse modeling technique (Li et al., 2019), the robustness of which is demonstrated by evaluation against multiple independent in situ measurements. The IASI-NH3 dataset was applied to optimize NH3 emission estimates from the 2011 National Emissions Inventory (2011 NEI) using the Community Multiscale Air Quality Modeling System (CMAQ) and its adjoint model at a 36 km × 36 km resolution. The multiphase adjoint model for CMAQ v5.0 was developed recently, including full adjoints for gas-phase chemistry, aerosols, cloud process, diffusion, and advection (Zhao et al., 2020). Both process-by-process and full adjoint model evaluations show reasonable accuracy based on agreements between the adjoint sensitivities and forward sensitivities (Zhao et al., 2020). Previous inversion-based NH3 emission constraints using in situ measures are limited by the spatial coverage and representativeness of the measurements (Gilliland et al., 2006; Henze et al., 2009; Paulot et al., 2014;). Zhu et al. (2013) first attempted to optimize the NH3 emission inventory using NH3 derived from the Tropospheric Emission Spectrometer satellite at 2×2.5 resolution (Zhu et al., 2013). Inverse modeling at such a coarse resolution is limited to refining regional emissions. Similar to the inversion using CrIS NH3 measurements (Cao et al., 2020), inversion with the IASI-NH3 dataset allows us to perform the optimization at a finer resolution with its daily global spatial coverage. Furthermore, the hybrid inversion approach adopted in this study allows us to calculate full adjoint sensitivities online instead of using approximated sensitivities from the offline simulations (Zhu et al., 2013; Cao et al., 2020). The performance of our optimized estimates and the 2011 NEI are evaluated and compared based on in situ observed ambient NH3 concentrations and NH4+ wet deposition. Finally, by substituting the a priori NH3 emissions with the optimized emissions, we assess the subsequent changes in simulated ambient PM2.5 concentrations and nitrogen deposition exceedances.

2 Materials and methods

2.1 IASI-NH3 observations

NH3 column densities retrieved from IASI on board the Metop-A satellite are assimilated to constrain spatially resolved NH3 emissions using the 2011 NEI as the a priori inventory (Clarisse et al., 2009; Van Damme et al., 2014; USEPA, 2014). The polar sun-synchronous satellite has a 12 km diameter footprint at nadir and a bidaily global coverage. Only observations from the morning pass around 09:30 local standard time (LST) are used due to more favorable thermal contrast and smaller errors as compared to the night pass around 21:30 LST. A comparison between the IASI-NH3 data and ground-based Fourier transform infrared (FTIR) observations shows a correlation between the two with r=0.8 and the slope = 0.73, indicating a tendency of IASI-NH3 to underestimate the FTIR observations (Dammers et al., 2016). A comparison between IASI-NH3 and airborne measurements also indicated an underestimation in California, while the comparison between IASI-NH3 and ground observation from the Ammonia Monitoring Network (AMoN) indicated an overestimation (Van Damme et al., 2015a; NADP, 2014). Overall, the evaluations show broad consistency between IASI-NH3 and other independent measurements, with no consistent biases identified. These evaluations were based on previous datasets. Here we use a new version that relies on another retrieval algorithm, which among other things has better performance for measurements under unfavorable conditions (Whitburn et al., 2016; Van Damme et al., 2017).

Specifically, the NH3 products for 2011 from ANNI-NH3-v2.2R-I datasets were used (Van Damme et al., 2017). The algorithm relies on the conversion of hyperspectral range indices to NH3 column density using a neural network that takes into account 20 input parameters, characterizing temperature, pressure, humidity, and NH3 vertical profiles. A relative uncertainty estimate is provided along with each of the NH3 vertical column densities in the dataset. Small negative columns are possible – and these are valid observations, needed to reduce overall biases in the dataset. As the retrieval is unconstrained, no averaging kernels are calculated. We therefore directly compare the IASI-NH3 column density with the simulated column density in CMAQ. Such comparison may be biased because the sensitivity of retrieved NH3 column densities to NH3 concentrations is height-dependent (typically peaks around 700–850 hPa) (Dammers et al., 2017; Shephard et al., 2015). Although the CMAQ-simulated NH3 columns are also most sensitive to NH3 concentration changes between 700 to 900 hPa (Fig. S1), we cannot quantify the relating uncertainties without knowing the averaging kernels. Without information on averaging kernels, differences between NH3 vertical profiles in CMAQ and the ones used for retrieval may also contribute to the bias between retrieved and modeled column densities, depending on the magnitude of differences (Whitburn et al., 2016).

The retrieved NH3 columns densities are regridded to the 36 km by 36 km CMAQ grid for 4D-Var data assimilation and 216 km by 216 km resolution (a six-grid-by-six-grid CMAQ simulation grid matrix) for iterative mass balance (Fig. 1). The mean column density (Ωo) is calculated as the arithmetic mean of all retrievals with their centroids falling in the same grid cell, following the recommendation that the unweighted mean is preferred for the updated version of IASI-NH3 as error-weighting can lead to biases (Van Damme et al., 2017). The error (molec cm−2) corresponding to the mean column density in each grid is calculated as

(1) σ = σ i × Ω i 2 n - 1 ,

where σ is the mean error (molec cm−2), Ωi is the ith retrieval of NH3 column density from IASI-NH3 Level 2 data, σi is the relative error associated with each Ωi as reported, and n is the number of retrievals within each grid cell during the defined time period. For 4D-Var inversion and IMB inversion, daily and monthly means and errors are calculated, respectively.

Figure 1IASI monthly average NH3 column density in April, July, and October 2011 at 36 km by 36 km (a, b, c) and 216 km by 216 km (d, e, f) resolutions within the model simulation domain of this study. The average relative error associated with the column density is shown in the corner of each plot.

The observations from April, July, and October are used to constrain the monthly NH3 emission estimates in corresponding months from 2011 NEI. Limited by the high computational cost of adjoint-model-based inversion, the optimization is only performed for the 3 months selected instead of a full year. Observations from winter months are not used because they are too noisy when the thermal contrast is low (Dammers et al., 2016).

2.2 NH3 emission from 2011 NEI

The EPA 2011 NEI is used for a priori emission estimates. Major NH3 sources include livestock waste management, fertilizer application, mobile sources, fire, and fuel combustion, with the majority being emitted by the first two sources. Specifically, the emissions from livestock waste management are estimated based on county-level animal population data and process-based daily emission factors. Emissions from fertilizer applications are estimated based on county-level fertilizer quantities and fixed emission factors, following the CMU Ammonia Model (USEPA, 2015). The NH3 emissions over Mexico and Canada are derived from the simulation results of a fully coupled bi-directional agroecosystem and chemical transport model (FEST_C_EPIC_CMAQ_BIDI) (Shen et al., 2020). Emissions for other species also come from the 2011 NEI.

2.3 CMAQ and its adjoint

We use CMAQ v5.0 (Byun and Schere, 2006; USEPA, 2012) and its adjoint (Zhao et al., 2020), driven by meteorological fields produced from the Weather Research and Forecasting (WRF) Model v3.8.1 with grid nudging using the North American Regional Reanalysis dataset (NOAA, 2019). The simulated meteorological fields show good agreement with surface observations (Fig. S2) (NOAA, 2020). The CB05 chemical mechanism was adopted for gas-phase chemistry (Yarwood et al., 2005). The model implements ISORROPIA-II in the aerosol module (AERO06) to calculate the gas–particle partitioning of NH3 and NH4+ (Fountoukis and Nenes, 2007). The simulation domain covers the contiguous US (CONUS) and part of Canada and Mexico with a 36 km by 36 km horizontal resolution and 13 vertical layers extending up to 14.5 kPa (∼16 km) (Fig. 1). To evaluation CMAQ model performance, the simulated gas–particle partitioning ratio of NH3–NH4+ and NH4+ deposition is compared with observations from AMoN, the Clean Air Status and Trends Network, and the National Atmospheric Deposition Program (NADP) (Figs. S3 and S4). CMAQ captures the overall spatial pattern of these governing processes for atmospheric NH3 abundance, considering the uncertainties in emissions, model parameters, and meteorological fields. Expanded evaluation of CMAQ model performance in simulating gas–particle partitioning and nitrogen deposition has been conducted in previous studies (Chen et al., 2019, 2020). Monthly simulations are conducted for April, July, and October in 2011 with a 10 d spin-up for each month.

2.4 Hybrid inversion approach

We chose the hybrid inversion approach to combine the advantage of the faster computational speed of the mass balance method and the better optimization performance of the 4D-Var method. The first step is to apply the IMB approach to adjust the a priori (2011 NEI) NH3 emission at 216 km by 216 km resolution (referred to as the coarse grid hereafter) based on the ratio between the monthly averaged observed (Ωo) and simulated (Ωa) NH3 column density at the satellite overpassing time, iteratively. At each iteration, the emission in each grid cell is scaled by the ratio following the equation below:

(2) E t = Ω o Ω a × E a ,

where Et and Ea are the new and a priori emission estimates, respectively. The method has been described in detail in previous studies (Li et al., 2019; Cooper et al., 2017; Martin et al., 2003). The IMB is applied at the coarse grid so that the NH3 column will be dominated by the local emissions instead of transport from neighboring grids (Li et al., 2019). The coarse resolution also reduces the uncertainty associated with IASI-NH3 as the number of retrievals increases in each grid cell. For grid cells with mean relative error larger than 100 %, the satellite observations are considered to be too noisy to provide useful constraints and the a priori emission estimates are retained. The iteration stops when the normalized mean square error either decreases by less than 10 % or begins to increase. The final scaling factor (ε0) for each grid cell is the multiplication of the scaling factors derived at each iteration and downscaled to 36 km by 36 km resolution by assigning the same value to the six-by-six grid matrix. This scaling factor is applied to the 2011 NEI emissions to create the revised a priori estimate for the 4D-Var inversion.

Next, the 4D-Var inversion is performed. The solution of the optimization problem is sought iteratively by minimizing the cost function (J) defined as the combination of error-weighted, squared difference between the emission scaling factor and unity and the error-weighted, squared difference between IASI-NH3 and the simulated column density, as below:

(3) J = γ ε i - ε 0 T S a - 1 ε - ε 0 + Ω o - F ( ε ) T S o - 1 ( Ω o - F ( ε ) ) .

ε is the monthly emission scaling factor to be optimized at each iteration where ε=logEt/Ea on the 36 km by 36 km CMAQ grid, consisting of 6104 overland grid cells in the CONUS. Sa and So are error covariance matrices for the a priori emission estimates and IASI-NH3 retrievals, respectively. With limited information on the spatial correlation of the error covariance, the two matrices are assumed to be diagonal (Paulot et al., 2014; Zhu et al., 2013). For So, the grid average absolute error is used to represent the observational error. Our test shows that negative Ωo will lead to a continuous decrease in the adjusted emission for the grid cell because modeled column density cannot become negative. To limit the influence of these negative Ωo, their original weights are multiplied by 0.01. For Sa, the uncertainty in each grid cell is assumed to be 100 % of the a priori emissions. F(ε) is CMAQ-simulated NH3 column density sampled at the satellite passing time if there is at least one IASI-NH3 retrieval in that grid cell; γ is the regularization factor balancing the relative contribution of the a priori emission inventory and IASI-NH3 retrievals to the J value. γ is chosen to be 800 for April and 500 for July and October based on the L-curve criteria (Hansen, 1999) (Fig. S5).

The gradients of the cost function to NH3 emissions are calculated by the CMAQ adjoint model. In each iteration, the emission-weighted monthly averaged sensitivities in each grid cell are supplied to the L-BFGS-B optimization routine contained in the “optimr” package in R to find the scaling factors that will achieve the minimum of the cost function (Zhu et al., 1997; Byrd et al., 1995). NH3 column density is re-simulated using adjusted emissions by the new set of scaling factors. The iteration process is terminated when the decrease in J is less than 2 % or the local minimum is reached (Li et al., 2019; Zhu et al., 2013).

2.5 Posterior evaluation

The posterior emissions are evaluated by comparing the model simulation from optimized emissions with observations. Simulated results are compared with ambient NH3 concentrations from AMoN (NADP, 2014) and the NH4+ wet deposition from NADP (NADP, 2019). The simulated NH3 concentration in ppmv is converted to micrograms per cubic meter (µg m−3) using local temperature and pressure from the model meteorological inputs. For evaluation against the NH4+ wet deposition, the simulated deposition is scaled by the ratio between measured and simulated precipitation to eliminate the bias introduced by precipitation fields (Appel et al., 2011).

3 Results

3.1 Optimization performance evaluation

The optimized NH3 emissions reduce the bias in the NH3 columns between the satellite observation and the model prediction as shown by the decrease in the values of normalized root mean square error (NRMSE) and normalized mean biases (NMBs) in Fig. 2. There are negative biases using 2011 NEI in all 3 months, especially in areas with high emission rates. Although the IMB inversion can lower the NRMSE, it tends to over-adjust and introduce a positive bias, likely because of the coarse resolution and neglect of the impact of transport. The 4D-Var inversion effectively decreases the positive bias and further reduces the NRMSE. The cost function value reduces by 85, 46, and 38 % with the 4D-Var inversion in April, July, and October, respectively. We find that it is more challenging to adjust the emissions in April than in the other 2 months because of the greater differences in the magnitude and the spatial distribution of the emissions. The optimized NH3 emission successfully captures the high NH3 column density in the Southern States (Texas and Oklahoma), reducing the NRMSE by half in that region. Despite the general improvement in the model performance, negative biases in July increase in California's San Joaquin Valley. Scaling up the emission in the San Joaquin Valley will result in high NH3 concentrations downwind even when the local NH3 emissions downwind are zeroed, whereas the IASI-NH3 observed concentrations downwind are low. The transported hotspot downwind of the San Joaquin Valley in CMAQ only occurs in July, suggesting near-field removal may not be captured at the current resolution, and warrants further investigation. Grid-by-grid comparison between model-simulated NH3 column density using the a priori and optimized estimates with IASI-NH3 shows improved agreement in both high- and low-emission grid cells after optimization (Fig. S6). It shows that the hybrid inversion approach can alleviate the weakness of direct 4D-Var inversion, which tends to over-adjust high-emission regions and under-adjust low-emission regions, mainly because the IMB inversion provides a better initial state.

Figure 2CMAQ-simulated monthly average NH3 column density for April, July, and October 2011 using the a priori emissions (a, b, c), the emissions adjusted by IMB (d, e, f), and the final optimized emissions using the hybrid approach (g, h, i). For comparison with the IASI-NH3 retrievals, simulated NH3 columns at the passing time were derived when there were observations in that grid cell. Normalized root mean square error (NRMSE) and normalized mean bias (NMB) between the simulated values and IASI-NH3 are provided. Residue map (IASI-NH3 simulated NH3 column densities) is shown in the corner of each plot.

The IMB inversion took three iterations to achieve the convergence condition for each month, and subsequently the 4D-Var inversion took 10, 4, and 6 iterations for April, July, and October, respectively. Fewer iterations are needed with the hybrid approach than the direct 4D-Var inversion, which typically takes up to 15 to 20 iterations of adjoint simulation (Paulot et al., 2014; Zhang et al., 2018a). The CPU time of a forward simulation is only one-fifth of an adjoint simulation. In total, the CPU time required by the hybrid approach is expected to be one-third to two-thirds lower than the direct 4D-Var inversion approach.

3.2 Optimized estimate of NH3 emissions

The monthly total NH3 emission in the CONUS increases by 35 % in April, 18 % in July, and 10 % in October for the optimized estimates. Spatially, the distribution for high-emission regions shifts from the Midwest in the 2011 NEI to the Southern States in the optimized estimates in April, whereas the hotspot regions remain consistent in July and October (Fig. 3). Regional total emissions are summarized according to the USDA farm production regions, which define the areas with similar crop production activities (Cooter et al., 2012). In general, the regional variation of NH3 emissions in April is dominated by fertilizer application. The optimized estimates in the Corn Belt and Lake States regions are lower than the 2011 NEI, where high contributions from fertilizer applications were estimated. In contrast, the optimized estimates are 2–3 times higher than the 2011 NEI estimates in the Delta States and Southern States, where the a priori estimates for NH3 emission from fertilizer application are low. The higher NH3 emission estimates in the Southern States are driven by the enhanced NH3 column densities from IASI over that region. IASI-NH3 column densities are higher in 2011 than those in adjacent years (Fig. S7), which coincides with the higher surface temperature observed in 2011 (NOAA 2019) (Fig. S8). NH3 emission will increase due to enhanced NH3 volatilization from agricultural lands under warmer conditions (Bash et al., 2013; Shen et al., 2020). In fact, the optimized NH3 emission pattern in April is more consistent with the spatial pattern of inorganic nitrogen fertilizer estimated based on plant demand (Cooter et al., 2012). NH3 emission in 2011 estimated by CMAQ with a NH3 bidirectional exchange model also predicted higher NH3 emission in the Southern States (Shen et al., 2020). The ratio between NH3 emission estimates in Southern States and those within the CONUS is 26 and 18 % in the optimized estimates and estimates including NH3 bidirectional exchange, respectively. In comparison, the ratio is only 10 % in the a priori NEI estimates, suggesting a potential low bias in 2011 NEI. In July, regional differences are smaller except for the Northern Plain and Mountain region. In the Northern Plain, the NH3 emission is 66 % higher in the optimized estimates, driven by the emission increase in hotspot areas with concentrated animal feeding operations (CAFOs) (USDA, 2012; Van Damme et al., 2017, Clarisse et al., 2019). The potential bias in different sectors suggests the need for sectoral inversion when a larger observational dataset becomes available in the future. In October, the relative difference is less than 10 % in most of the regions, indicating that the 2011 NEI appropriately reflects the NH3 emission pattern. There is a significant increase in the NH3 emissions in Mexico during all 3 months. Such an emission increment is crucial to improving the model performance in both Mexico and the southwestern US. However, it was not a goal of this study to determine emissions biases in Mexico given the limited information on NH3 emissions.

Figure 3The spatial distribution of monthly total NH3 emission from the a priori (a, b, c) and optimized (d, e, f) estimates in April, July, and October. The total emission based on the a priori and optimized estimates is summarized for each USDA farm production region (g, h, i). The source contributions to total emission are shown for the a priori estimates.

The total NH3 emissions in the optimized estimates are 623, 564, and 335 Gg per month in April, July, and October, respectively. In comparison, the emission estimates in the 2011 NEI are 462, 475, and 304 Gg per month for the 3 months. Similar to a bottom-up agricultural NH3 emission inventory (MASAGE_NH3) and two inverse-model-optimized estimates based on NH4+ wet deposition, we find a higher emission in the spring season (Paulot et al., 2014; Gilliland et al., 2006), while others, including the NEI, estimate a summertime peak (Zhu et al., 2013; USEPA, 2015; Cooter et al., 2012; Cao et al., 2020). The large variation between different inventories warrants both improved information on bottom-up inventories and more observations to support inverse model optimization in the spring season. Better knowledge about agricultural activities and more independent ground and space observations are needed. Besides the a priori emission inventory and observational constraints, the inversion performance will also be affected by other processes (e.g., gas–particle partition, transport, cloud and precipitation, and dry and wet deposition) governing the atmospheric abundance of NH3. Future works refining the pertinent processes will also help improve the optimized NH3 emission estimates. It should also be noted that there are interannual variations in emission inventories developed for different years. The good spatial agreement with IASI-NH3 indicates that the 2011 NEI captures the NH3 emission pattern in general in these 2 months. Although the inversion is only applied for the selected 3 months, the simulated NH3 column densities using the a priori inventory are consistently lower than the IASI-NH3 observations in 2011 (Fig. S9), suggesting that the NH3 emission estimates in 2011 NEI may be biased low in other months, too.

3.3 Evaluation of the optimized emission estimates against independent datasets

The robustness of the NH3 emission optimization is evaluated by comparing the model outputs using both the a priori and optimized emission estimates with independent observations. The bias and uncertainties inherited in the CMAQ forward model and its adjoint, as well as the assumptions made about the uncertainties of the a priori emission inventory and IASI-NH3 observations, will all influence the robustness. Here, we choose to evaluate the outputs against (1) biweekly average ambient NH3 concentrations measured by AMoN and (2) weekly average NH4+ wet deposition measured by NADP (Fig. 4).

Figure 4Evaluation of the simulated NH3 surface concentration (a, b, c) and NH4+ wet deposition (d, e, f) against biweekly NH3 concentration observations from AMoN and weekly NH4+ wet deposition observations from NADP, respectively. The orange circles and blue dots represent comparison using the a priori and optimized NH3 emission estimates, respectively. Summary statistics including sample size (N), normalized mean bias (NMB), normalized root mean square error (NRMSE), least square error regression slope and intercept, and R square (R2) for all comparisons are listed below the plots.


In general, the optimized NH3 emission reduces the negative NMB when comparing the CMAQ outputs with AMoN NH3 concentration for all 3 months. There is a greater improvement at the high-concentration end than the low-concentration end because both the IASI satellite and the passive samplers at the AMoN sites have higher uncertainties in areas with low NH3 abundance (Van Damme et al., 2015a; Puchalski et al., 2011). Yet the NRMSE gets higher and R2 gets lower in April, indicating a higher spatial variation in the residuals. There is an over-adjustment for sites in Pennsylvania in April, where there is a hotspot observed by IASI on 14 and 15 April. The hotspot possibly came from a large transported plume at a higher altitude from the central US to Pennsylvania (Figs. S10 and S11), which is not measured by ground observations at AMoN sites at biweekly resolution. If that is the case, the hybrid inverse modeling framework would have difficulties in reproducing the long-range transport contribution for two reasons. First, local emissions in Pennsylvania would be enhanced in the IMB inversion, and inter-grid transport were neglected at 216 km by 216 km resolution. Second, the following 4D-Var inversion very likely reached a local optimal by adjusting emissions from local and surrounding grid cells near the observed hotspot rather than grid cells at distance. Furthermore, the IASI-NH3 column densities may be overestimated because vertical profiles with the highest concentrations near the surface were assumed in the retrieval process (Whitburn et al., 2016).

For evaluation against NADP observations, there is a noticeably improved agreement in April, with reduced negative NMB and reduced discrepancies for most of the data pairs. For July, the emission optimization only slightly improved the model performance. For October, the optimization increased the NMB from −1.8 to 4.8 %. This indicates that NH3 emission is not the dominant explanatory factor for bias in simulated NH4+ wet deposition that is commonly observed in chemical transport models (Appel et al., 2011; Paulot et al., 2014). A better representation of the cloud, precipitation, and deposition processes in the WRF Model and CMAQ is needed to close the gap between simulated and observed NH4+ deposition amount. Overall, the improved model operational performance for ambient NH3 suggests that the inverse model optimization applied in this study provides improvements in the NH3 emission estimates during all 3 months in most of the CONUS, except in Pennsylvania and surrounding regions in April. The hybrid inverse modeling technique may over-adjust local emissions in hotspots dominated by long-range transport.

4 Implications

4.1 Ambient aerosol concentration

As a major precursor of ambient aerosol formation, the NH3 emission inventory is believed to be a major source of uncertainty in PM2.5 assessment in several parts of the CONUS (Henze et al., 2009; Schiferl et al., 2014; Heald et al., 2012), which can further bias the source contribution assessments on PM2.5-related health impacts (Lee et al., 2015; Zhao et al., 2020). Comparison of the simulated PM2.5 mass concentration using the a priori and optimized NH3 emission estimates shows that the NH3 emission bias in April is a major factor for bias in the modeled PM2.5 concentration leading to high or low bias in ammonium nitrate (NH4NO3) formation (Fig. 5). The relative change of the monthly average PM2.5 concentration is over 5 % in one-fifth of the CONUS, including an increase in the Northeast, the Pacific West, the Rocky Mountains, part of Texas, and the Gulf Coast region, and a decrease in the Midwest. For most of these regions, over 90 % of the change is driven by the change in concentration of NH4+ and NO3-.

Figure 5The changes in monthly average PM2.5, NH4+, and NO3- mass concentration in April due to the NH3 emission adjustment in the optimized estimates. The change is defined as concoptimized−conca priori, where concoptimized and conca priori represent the simulated monthly average mass concentration using the optimized and a priori NH3 emission estimates, respectively. The difference between the observed NH4+ and NO3- mass concentration and simulated concentrations using the a priori NH3 emission (concobs−conca priori, where concobs represents the observed monthly average mass concentration) is overlaid using colored dots with the same color scheme.

Comparison of the simulated monthly average NH4+ and NO3- concentration using the a priori estimates against ambient monitoring network data (USEPA, 2018) shows that there is a high bias in the Midwest region and Pennsylvania state, and a low bias for the rest of the sites (Table 1). Simulations using the optimized NH3 emission estimates reduce the high bias in the Midwest region but exacerbate the high bias in Pennsylvania state and the surrounding areas. For the other sites, the impact of optimization is mixed but minor in general.

Table 1Statistical summary of the correlation between simulated monthly average NH4+ and NO3- concentrations and observations in April*.

* The correlation between observed concentrations and simulated ones based on a priori and optimized NH3 emission estimates is compared. The sites are grouped as the Midwest region, Pennsylvania state and surrounding areas, and other areas.

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For the Midwest, our optimized NH3 emission is 12 % lower than the 2011 NEI, leading to a 5–30 % decrease in NH4+ and NO3- concentration. Overestimation of NO3- in the Midwest has been recognized in previous model evaluations. Previous studies have attempted to moderate the high bias by lowering the nitric acid (HNO3) concentration through either lowering both the daytime and nighttime HNO3 formation rate or raising the deposition removal rate (Heald et al., 2012; Zhang et al., 2012; Walker et al., 2012). It was found that such modification in the model parameterization cannot fully account for the overestimation (Heald et al., 2012; Zhang et al., 2012; Walker et al., 2012). Our study implies that the springtime overestimation can partly be explained by the overestimation in NH3 emissions which drives the high bias in NH4NO3 formation.

The large increase of the NH4NO3 concentration in Pennsylvania state and the surrounding areas is due to the over-amplified local NH3 emissions in the optimized estimates to match the high NH3 column density in IASI-NH3 2011, as discussed earlier. It leads to a higher magnitude of biases in NH4+ and NO3- concentration as compared to ground measurements. The fact that the simulated ambient NH3 concentration, NH4+ concentration, and NH4+ wet deposition using the optimized NH3 estimates are biased high in comparison with independent ground measurements suggests the enhanced NH3 abundance observed from IASI is possibly driven by long-range transport at higher altitudes instead of local surface emissions.

For the rest of the CONUS, there is only a slight impact of the optimization on simulated NH4NO3 formation. For example, although the NH3 emission is doubled in the San Joaquin Valley in California, the modeled NH4+ and NO3- concentrations are still biased low using the optimized estimates. A sensitivity test using GEOS-Chem shows that the San Joaquin Valley region is nitric-acid-limited instead of ammonia-limited (Walker et al., 2012), suggesting that there is an underestimation in HNO3 formation. A comparison of the simulated and measured speciated PM2.5 shows that there is a low bias in non-volatile cation concentrations at the sites in the San Joaquin Valley, limiting the formation of NH4NO3 through gas–particle partitioning (Chen et al., 2019). Thus, attempts to close the gap between the simulated and monitored NH4+ and NO3- concentrations by scaling NH3 emission alone are ineffective and might lead to an overestimation in local NH3 emissions.

For July and October, there is a very limited difference between the simulated PM2.5 concentration using the optimized and a priori NH3 emission estimates, as expected, because the change in NH3 emission is minor. There are only 1 and 4 % of the CONUS with a relative change in PM2.5 concentration over 5 %, respectively. This result shows that the uncertainty in NH3 emission estimates is moderate and is not a major contributor to biases in modeled PM2.5 in July and October.

4.2 Reactive nitrogen deposition

The uncertainties in NH3 emission inventory also impact the reactive nitrogen (Nr) deposition assessment, which informs the ecosystem impacts evaluation and effective mitigation actions (Ellis et al., 2013). To evaluate the impact of the NH3 emission optimization on simulated Nr deposition, the Nr deposition amount simulated using optimized and a priori emission estimates is analyzed in all biodiversity-protected areas designated by the USGS (Fig. S12) within the CONUS (USGS, 2018). In total, the Nr deposition increased by 27, 9, and 5 % on average in these protected areas in April, July, and October, respectively. A regional comparison based on the Level I ecoregions (Pardo et al., 2015) shows that the deposition increment is the highest in the Tropical Wet Forests (+64 %), followed by the Great Plain region (+46 %), in April (Fig. 6). Although the overall increase is small in July and October, the increment can be high in individual ecoregions, including Southern Semiarid Highlands (+95 % in July) and Temperate Sierras (+62 % in July). In addition to the increment in deposition amount, higher NH3 emission, especially in intensive agriculture regions, may indicate higher source contribution from agricultural NH3 than previous estimates (Lee et al., 2016).

Figure 6The changes in the simulated monthly reactive nitrogen (Nr) deposition amount in protected areas for biodiversity conservation caused by the emission adjustment in April, July, and October. For each month, the left bar is for the a priori deposition amounts and the right bar is for the optimized deposition amounts. The deposition is grouped for 10 Level I ecoregions defined by the Commission for Environmental Cooperation, including Northern Forests (NF), Great Plains (GP), Northwestern Forested Mountains (NFM), Marine West Coast Forest (MWCF), North American Deserts (NAD), Mediterranean California (MC), Southern Semiarid Highlands (SSH), Temperate Sierras (TS), and Tropical Wet Forests (TWF).

Driven by the increase in the reduced form of Nr (NH3 and NH4+) deposition, a higher share of the reduced form of Nr to the total Nr deposition is found in most of the ecoregions for all 3 months than in the NEI-based estimates. More detrimental impacts on sensitive species and biodiversity are expected when this change in dominant Nr form is considered in addition to the increase in magnitude because the growth of many sensitive plant species will be inhibited by a high NH4+-to-NO3- ratio in soil and water (Bobbink and Hicks, 2014).

5 Conclusions

We apply the newly developed multiphase adjoint of the CMAQ v5.0 chemical transport model and NH3 column observations from the satellite-borne IASI to optimize NH3 emissions estimates in the CONUS using a hybrid inversion modeling approach. The approach consists of a coarse-resolution iterative mass balance inversion (216 km by 216 km) and a fine-resolution 4D-VAR inversion (36 km by 36 km) and is performed using IASI-NH3 observations in April, July, and October. The hybrid approach overcomes the over-adjusting problem for high-emission areas in the direct 4D-Var method and reduces the computational cost, but it may introduce over-adjustment in special cases where the NH3 abundance is dominated by transport instead of local emissions.

We use the NH3 emission from 2011 NEI, commonly used in regional and national simulations and assessments as the a priori emission. We find that the optimized NH3 emission inventory differs greatly with the 2011 NEI in April. The emission in the Midwest is overestimated and the emission in the Southern States is underestimated in the 2011 NEI. Overall, the optimized emission is 35 % higher in April. The optimized emission estimates in July and October are also higher (18 and 10 %) than the 2011 NEI estimates, but the spatial distribution agrees well. The IASI-NH3 observations indicate a consistent underestimation of NH3 emissions in California's San Joaquin Valley in all 3 months; however, the inverse modeling fails to properly scale up the emissions in July. The evaluation of simulation outputs against ground measurements including ambient NH3 concentrations from AMoN and NH4+ wet deposition from NADP shows that the optimized NH3 emission estimates reduce the NMB between model outputs and independent observations, especially in April. The NRMSE remains high, indicating (1) the potential to further optimize NH3 emission estimates when more representative observations of ambient NH3 abundance become available and (2) the need to address the uncertainties in other processes affecting the NH3 abundance, such as gas–particle partitioning, dry and wet deposition, and in-cloud processes.

Application of the optimized NH3 emission estimates also yields a better agreement between the simulated and observed PM2.5 concentration in April in the Midwest region by improving the model performance on simulated NH4+ and NO3-. This is consistent with previous findings that the uncertainty in NH3 emission is a key factor limiting the model performance of PM2.5. The optimized NH3 emission estimates in general increase the Nr deposition amount and the relative importance of reduced-form Nr, highlighting the importance of constraining NH3 emission estimates for accurately assessing nitrogen deposition and ecosystem health over sensitive regions.

Data availability

The IASI/Metop-A NH3 total column Level 2 data are available at the IASI portal provided by the AERIS data infrastructure (; ULB, 2018). Independent observations for evaluation – including surface NH3 concentrations, NH4+ wet depositions, and speciated PM2.5 concentrations – are available from the NADP website and Air Quality System (, NADP, 2014;, NADP, 2019;, USEPA, 2018).


The supplement related to this article is available online at:

Author contributions

AR and YC conceived the study. YC, AR, HZ, and JK contributed to the design the method. YC conducted the inverse modeling and data analysis. LC, PFC, and MVD are responsible for the IASI-NH3 data. SC, SZ, AH, MR, MT, DH, PP, JR, AN, AP, SN, JB, KF, GC, CS, TC, and AR developed the adjoint model of CMAQ. YC prepared the manuscript, with discussions and comments from HS, AR, JK, YH, SC, SZ, JS, and GP. All authors gave approval to the final version of the manuscript.

Competing interests

The authors declare that they have no conflict of interest.


Contents of this publication are solely the responsibility of the grantee and do not necessarily represent the official views of the supporting agencies. Further, the US government does not endorse the purchase of any commercial products or services mentioned in the publication.


The authors acknowledge the AERIS data infrastructure for providing access to the IASI data in this study. ULB has been supported by the Belgian State Federal Office for Scientific, Technical and Cultural Affairs (Prodex arrangement IASI.FLOW). Lieven Clarisse and Martin Van Damme are respectively research associate and postdoctoral researcher with the Belgian F.R.S-FNRS.

Financial support

This research has been supported by the United States Environmental Protection Agency (grant no. R83588001), the National Aeronautics and Space Administration (grant no. NNX16AQ29G), and the China Scholarship Council (grant no. 201606010393).

Review statement

This paper was edited by Bryan N. Duncan and reviewed by two anonymous referees.


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Short summary
Ammonia (NH3) emissions can exert adverse impacts on air quality and ecosystem well-being. NH3 emission inventories are viewed as highly uncertain. Here we optimize the NH3 emission estimates in the US using an air quality model and NH3 measurements from the IASI satellite instruments. The optimized NH3 emissions are much higher than the National Emissions Inventory estimates in April. The optimized NH3 emissions improved model performance when evaluated against independent observation.
Final-revised paper