Quantifying Nitrous Oxide Emissions in the U.S. Midwest: A Top‐Down Study Using High Resolution Airborne In‐Situ Observations

The densely farmed U.S. Midwest is a prominent source of nitrous oxide (N2O) but top‐down and bottom‐up N2O emission estimates differ significantly. We quantify Midwest N2O emissions by combining observations from the Atmospheric Carbon and Transport‐America campaign with model simulations to scale the Emissions Database for Global Atmospheric Research (EDGAR). In October 2017, we scaled agricultural EDGAR v4.3.2 and v5.0 emissions by factors of 6.3 and 3.5, respectively, resulting in 0.42 nmol m−2 s−1 Midwest N2O emissions. In June/July 2019, a period when extreme flooding was occurring in the Midwest, agricultural scaling factors were 11.4 (v4.3.2) and 9.9 (v5.0), resulting in 1.06 nmol m−2 s−1 Midwest emissions. Uncertainties are on the order of 50 %. Agricultural emissions estimated with the process‐based model DayCent (Daily version of the CENTURY ecosystem model) were larger than in EDGAR but still substantially smaller than our estimates. The complexity of N2O emissions demands further studies to fully characterize Midwest emissions.

. Analyses of the isotopic composition of N 2 O indicate that the observed rise in global atmospheric N 2 O concentrations is mainly caused by the increased application of N-fertilizers (Park et al., 2012).
Bottom-up estimates, such as the Emissions Database for Global Atmospheric Research (EDGAR, 2020), use emission factors and activity data to calculate emissions. Agricultural practices (e.g., fertilizer application, crop type) as well as meteorological and soil conditions (e.g., precipitation, soil moisture) directly influence emissions, resulting in large temporal variability in N 2 O surface fluxes (Stehfest & Bouwman, 2006). Process-based models like DayCent (Daily version of the CENTURY ecosystem model) provide a more sophisticated approach for estimation of N 2 O emission by simulating soil processes based on various environmental drivers. Nevertheless, fluxes at regional scale are still highly uncertain due to insufficient direct observations (Reay et al., 2012).
The U.S. Midwest is one of the most intensively cultivated agricultural regions worldwide (FAO, 2020; US-DA-NASS, 2020), thus contributing significantly to global anthropogenic N 2 O emissions (Miller et al., 2012). Previous top-down studies indicate that emissions in the Midwest are underestimated by EDGAR, but are highly uncertain on the magnitude of this underestimation (Chen et al., 2016;Fu et al., 2017;Griffis et al., 2013;Kort et al., 2008;Miller et al., 2012). Kort et al. (2008) showed that EDGAR version 32FT2000 underestimates emissions in May to June 2003 by a factor of 2.62 over the central U.S. and southern Canada. Miller et al. (2012) derived scaling factors of 6.1 and 10.1 for EDGAR version 4 for June 2004 and June 2008, respectively. Fu et al. (2017) concluded even higher scaling factors for agricultural EDGAR version 4.2 emissions in the Corn Belt region of the Midwest, with scaling factors of 19.0-28.1 in June 2010. These described top-down studies used tall tower measurements, characterized by long time series over several months but limited in their spatial coverage. Only Kort et al. (2008) used aircraft-based flask measurements, which provide some spatial (central U.S. and southern Canada) but limited temporal (May to June 2003) coverage. The large range in the quantitative results show that Midwest N 2 O surface fluxes are underestimated by EDGAR inventories, but their true values are highly uncertain.
In this study, we quantify N 2 O emissions for several flights conducted in parts of the U.S. Midwest in October 2017 and June/July 2019 with a top-down approach. Unlike previous studies which have relied on observations with limited spatial coverage, this study uses continuous airborne in-situ measurements of N 2 O. By combining these observations with forward model simulations, we optimize agricultural fluxes from EDGAR version 4.3.2 and version 5.0 to quantify Midwest N 2 O emissions. The employed method was already successfully applied in several methane top-down studies (Barkley et al., 2017(Barkley et al., , 2019a(Barkley et al., , 2019b. The derived emission rates are finally compared to flux estimates of direct soil emissions produced with EDGAR and the biogeochemical model DayCent (Del Grosso et al., 2001, 2011Parton et al., 1998).

Observational Data
We use measurements from the Atmospheric Carbon and Transport-America (ACT-America) campaign. During the fall 2017 (October 10-November 13) and summer 2019 (June 17-July 27) field deployments, we collected ∼60 h of in-situ data onboard NASA's C-130 with an Aerodyne Quantum Cascade Laser Spectrometer (QCLS) measuring N 2 O mole fractions (among others) at 2 Hz with an uncertainty of 0.8 ppb (Kostinek et al., 2019). Every 3-10 min in-flight calibrations were performed using standards that were cross-calibrated after the campaign against NOAA/GML standards traceable to the NOAA-2006A scale (Hall et al., 2007). Additionally, during each flight 6-12 whole-air flask samples were taken by NOAA/GML and analyzed for trace gases including N 2 O with an uncertainty of 0.4 ppb (Baier et al., 2020;Sweeney et al., 2015Sweeney et al., , 2018. Those were merged into the QCLS time series to fill any data gaps. For this study, we selected four flights from 2017 (October) and six flights from 2019 (June/July). For each flight, the C-130 flew transects well within the planetary boundary layer (PBL) (∼1,000 ft above ground level (AGL)) for at least 45 min during which air above the Midwest was sampled. Figure 1a shows the selected transects, color-coded with observed N 2 O dry air mole fractions. Mole fractions up to 341 ppb were measured ( Figure 1b). We are not aware of comparable continuous N 2 O measurements spanning most of the Midwest across two seasons, highlighting the unique opportunity to quantify Midwest emissions with these data.

Model Setup
The Weather Research and Forecasting model with chemistry enabled (Grell et al., 2005) is used to propagate N 2 O enhancements emitted from emission inventories (Section 2.3) through the atmosphere. Initial N 2 O concentrations and the inflow at the boundaries of the model domain are set to zero. Thus, we simulate only enhancements caused by emissions within the model domain. We treat N 2 O as a passive tracer due to its long atmospheric lifetime of ∼116 years (Prather et al., 2015). The model domain consists of an outer and inner domain with a horizontal resolution of 15 km × 15 km and 3 km × 3 km, respectively. The outer domain, centered over the Midwest, covers nearly the whole continental U.S., northern Mexico, and southern Canada (Figure 2a), whereas the extent and position of the inner domain is chosen separately for each flight so that the PBL transects are spaciously encapsulated. We perform each simulation with three different meteorological initial and boundary conditions: The fifth generation atmospheric reanalysis data (ERA5, 2017;Hersbach et al., 2020), the North American Regional Reanalysis (NARR, 2005), and the Global Data Assimilation System Final analysis (GDAS-FNL, 2015). As in Barkley et al. (2019a), we use these different simulations to estimate model transport errors (Díaz-Isaac et al., 2018). The SupportingInformation(SI) provides additional information about the model setup.

Emission Inventories
The prior N 2 O emission estimates for the optimization were obtained from EDGAR version 4.3.2 (ED-GAR4.3.2, 2017; Janssens-Maenhout et al., 2019) and version 5.0 (Crippa et al., 2020;EDGAR5.0, 2019). For this study the different sectors in the inventories were merged into three main sectors: agricultural E AGR , anthropogenic nonagricultural E nonAGR , and natural emissions E N (see SI). We assume that these three sectors cover all N 2 O emissions in the model domain. EDGAR4.3.2 and EDGAR5.0 provide monthly resolved N 2 O fluxes from anthropogenic sources (E AGR and E nonAGR ) on a 0.1° × 0.1° grid for 2012 and 2015, respectively, but do not include fluxes from natural sources. Hence, we supplemented both versions with yearly E N on a 1° × 1° grid from EDGAR version 2.0 (EDGAR2; Olivier et al., 1996Olivier et al., , 1999. With the process-based, biogeochemical model DayCent we estimated daily direct N 2 O soil emissions from cropland and grassland on a 0.5° × 0.5° grid in the Midwest from 2011 to 2015, which were aggregated to a monthly time step. The model simulates fluxes of carbon and nitrogen between the atmosphere, vegetation, and soil thus deriving N 2 O emissions. Incorporating several environmental drivers, including weather patterns, agricultural practices, soil characteristics, and crop features, this approach provides a more ECKL ET AL. sophisticated estimate of soil emissions than the emission factor-based EDGAR. The GHG inventory of the United States Environmental Protection Agency (EPA, 2020) uses DayCent estimates of direct soil emissions for emission reporting of agricultural soil N 2 O to the UN Framework Convention on Climate Change. DayCent does not calculate emissions from manure management, agricultural waste burning, indirect soil emissions, and those associated with minor crops such as vegetables. The EPA inventory quantifies these sources with an emission factor approach. We estimate their contribution by employing the yearly, national estimates from EPA, calculating their fraction of the EPA direct soil emissions, and adding them to our monthly estimates. As a result, our DayCent inventory accounts for the total agricultural emissions, but not the spatial distribution of agricultural sources which are not estimated by DayCent. A qualitative comparison of EDGAR emission maps supports the underlying assumption that the spatial distribution of soil and other agricultural emissions are similar.

Optimization Technique
To solve for N 2 O emissions, we use an approach similar to the optimization described in Barkley et al. (2017). First, we calculate the observed N 2 O enhancements by subtracting a background from the measured absolute mole fraction. For each campaign we derive one background by taking the second percentile of all PBL transects of the entire campaign (see SI). The background is defined campaign-wise rather than transect-wise because during some transects we were not able to measure background mole fractions as we started a transect within a plume and did not exit the plume inside of the PBL (Figure 1b).
We then compare modeled N 2 O enhancements from our prior emissions (E AGR + E nonAGR + E N ) to the observed enhancements. Differences between both are then minimized for each flight by scaling agricultural ECKL ET AL.  emissions E AGR with a factor F AGR thus quantifying emissions. This process relies on the assumption that the discrepancy between model and observation is primarily driven by errors in E AGR . As agricultural emissions are the dominant N 2 O source in our flights, we assume that errors in E nonAGR and E N are inconsequential to the overall solution. The complexity of N 2 O soil emissions suggests that E AGR exhibits a much higher uncertainty than other sources (Butterbach-Bahl et al., 2013), supporting the presented approach.
As an equation, this optimization technique is described by calculating F AGR through the minimization of the following cost function: A obs and A mod are the time integral along a transect of observed and modeled enhancements, respectively (e.g., area below graph in Figure 3a). A mod consists of an agricultural portion A AGR scaleable with F AGR , a non-agricultural anthropogenic portion A nonAGR , and a natural portion A N . We compare integrals rather than enhancements because we are interested in the amount of N 2 O emitted to the atmosphere. Neither the model transport nor the inventory is perfect and even small uncertainties in either of them could cause a ECKL ET AL.
10.1029/2020GL091266 5 of 11 shift or deformation in the alignment of the modeled plume relative to the observed plume. By minimizing the difference in the total N 2 O enhancements rather than the point-by-point absolute error, we preserve the capability to solve for total N 2 O emissions even when the modeled and observed plumes do not align. Due to the linearity between A AGR and the area averaged E AGR (see SI), a F AGR derived with Equation 1 denotes a F AGR -folded E AGR .

Uncertainty Assessment
We adopted the method of Barkley et al. (2019a) to assess uncertainties in our solutions. F AGR is affected by uncertainties in the following variables: 1. observed background mole fraction 2. A nonAGR 3. A N 4. model transport 5. model wind speed and PBL height (PBLH) 6. spatial distribution in EDGAR emissions We quantify the influence of uncertainties 1-4 with a Monte Carlo approach. For each flight, we repeat the optimization 10,000 times with a perturbed background mole fraction, A nonAGR , and A N . For the background we add a normal random number with μ = 0 ppb and σ = ± 0.5 ppb for 2017 and σ = ± 0.9 ppb for 2019 to the observation derived value. A nonAGR and A N are independently multiplied by a factor drawn from a normal distribution with μ = 1.0 and σ = ±0.21 and σ = ±0.42, respectively. To account for the model transport error, we randomly select one of the three model runs with different meteorological initial and boundary conditions, creating variability in the plume shape. The resulting spread in F AGR is used as its uncertainty. Explanations of the used uncertainties are in the SI.
The modeled wind speed and PBLH uncertainty (source 5) cannot be covered by the Monte Carlo simulation. Errors in these variables cause lower or higher simulated enhancements thus producing biases. Following Barkley et al. (2017), we correct for those biases by applying a correction factor based on the differences between the modeled and observed wind speed and PBLH. On average, the modeled wind speed and PBLH is 8 % and 3 % higher than observations, respectively. The impact of this correction on our results is insignificant (see SI).
Our final source of uncertainty relates to errors in the spatial distribution of the fluxes in the prior inventory and is difficult to quantify. However, the mapping of emissions in EDGAR is based on several high-resolution proxy data sets (Janssens-Maenhout et al., 2019). For this reason, we assume its spatial errors to be small. Given the insignificant difference between modeled and observed wind speeds and PBLH, the good agreement between modeled and measured plume structures support this assumption (see SI). Furthermore, because we quantify large areas and not point sources, slight misplacement in the inventory would only marginally affect our results. At the same time, missing or strongly misplaced fluxes would produce errors that are not considered in this study.  Figure 2b shows DayCent direct soil emissions in July 2015. Similar to EDGAR, the Midwest is a prominent source of N 2 O. We are not able to perform a detailed comparison of the spatial distributions in EDGAR and DayCent as both do not cover the same set of sources. However, in terms of the overall magnitude, DayCent estimates much higher surface fluxes compared to EDGAR, despite containing fewer sources (gridded total agricultural DayCent emissions are not available; Section 2.3).

Emission Inventory Comparison
ECKL ET AL. Figure 2c displays the monthly evolution of E AGR , E nonAGR , and E N averaged over the Midwest. Both EDGAR versions have an annual average E AGR of ∼0.10 nmol m −2 s −1 . However, unlike EDGAR5.0, EDGAR4.3.2 exhibits a strong seasonal cycle ranging from 0.05 nmol m −2 s −1 in winter up to 0.24 nmol m −2 s −1 in spring. In spring, when most N-fertilizer is applied, the amount peaks, followed by a plateau during summer at 0.09 nmol m −2 s −1 . The harvest season in fall features a local peak at 0.11 nmol m −2 s −1 . A future update of EDGAR5.0 will contain a seasonal cycle for some crop related emissions (Crippa et al., 2020). E nonAGR shows no significant change over the year and is on average 0.04 nmol m −2 s −1 in both versions. Natural soil emissions account for 0.02 nmol m −2 s −1 per month.

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From 2011 to 2015 DayCent emissions in the Midwest range between 0.23 and 0.35, 0.12-0.21, and 0.06-0.08 nmol m −2 s −1 in June, July, and October, respectively. June and July emissions are significantly larger than in EDGAR, despite excluding manure management, indirect soil, and agricultural waste burning emissions. DayCent's October emissions are within the magnitude of agricultural EDGAR emissions. We estimate total agricultural Midwest emissions from 2011 to 2015 by combining DayCent direct soil emissions and the EPA GHG inventory (Section 2.3), resulting in 0.32-0.48, 0.16-0.30, and 0.08-0.11 nmol m −2 s −1 in June, July, and October, respectively. In June/July this is on average over four/two times higher than EDGAR's E AGR . The 2012 emissions are significantly lower than in the other years causing the large range across years in the summer months. During this year, the most extensive drought since the 1930s occurred across a large swath of the U.S., including most of the Midwest, which lead to widespread harvest failure (NOAA-NCEI, 2020). This event might explain the low values and indicates that during an average climatological year DayCent emissions are at the upper end of the range. Furthermore, in contrast to EDGAR4.3.2 which states constant emissions in June and July, DayCent emissions are much higher in June than in July. Sweeney et al. (2015) derived annual N 2 O climatologies at Midwest sites from NOAA/ESRL Aircraft Network measurements and found highest N 2 O mole fractions in June, consistent with our DayCent estimates.

Model Optimization
Here, we provide an example of the model optimization process for October 10, 2017 (Figure 3a). In the eastern part of the Midwest, N 2 O enhancements up to 7 ppb were observed within the PBL. The below background values at the beginning of the time series occurred prior to the PBL transect in the free troposphere. Free tropospheric air might have a different history and hence different background which can lead to negative values if we subtract the PBL background. Model simulations with unmodified EDGAR emissions show only enhancements up to 1 ppb along the transect. However, by applying a correction factor F AGR of 8.3 the model is able to reproduce our measurements. Optimizations of the remaining days can be found in the SI. Figure 3b shows the mean and standard deviation for F AGR of the Monte Carlo simulations of the 10 research flights for the two EDGAR versions. As both inventories have a comparable spatial distribution, factors vary due to differences in total emissions. EDGAR4.3.2 correction factors are considerably higher for October 2017 and slightly higher for June/July 2019 than EDGAR5.0. For EDGAR4.3.2, F AGR ranges from 2.9 ± 1.5 to 11.3 ± 3.8 in 2017, with an average factor of 6.3 ± 4.6. EDGAR5.0 F AGR is calculated to be lower, ranging from 1.6 ± 0.8 to 6.8 ± 2.3, with an average factor of 3.5 ± 2.7. For 2019 we modified EDGAR4.3.2 with a F AGR between 5.5 ± 2.1 and 20.2 ± 6.3 and EDGAR5.0 between 4.9 ± 1.9 and 17.4 ± 5.5. On average this denotes an agricultural correction factor of 11.4 ± 6.6 and 9.9 ± 5.7 for EDGAR4.3.2 and EDGAR5.0, respectively. Altogether, both EDGAR versions exhibit a significant underestimation of agricultural emissions. Seasonal differences are likely one cause for the difference in correction factors between 2017 and 2019. Additionally, during the 2019 aircraft campaign, an extreme flooding event occurred that likely influenced our results (discussed below). Although EDGAR4.3.2 exhibits a seasonal cycle, its agricultural correction factor also varies considerably between 2017 and 2019. Hence, the Midwest seasonality is not captured in the EDGAR inventory, which appears to be caused by the flooding. Figure 3c

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Optimized emissions for June/July 2019 are 2-3 times higher compared to DayCent emissions. Despite this, DayCent emissions are closer to our optimized emissions compared to EDGAR during the same period. In contrast, DayCent and EDGAR emissions are both too low by a similar magnitude in October compared to our optimized results. Hence, as DayCent considers regional characteristics, it performs much better on the regional scale in the summer than the emission factor approach that is used in EDGAR. A more quantitative evaluation of DayCent would require flux calculations for 2017 and 2019 incorporating the corresponding regional conditions like weather, soil conditions, and N-fertilizer application rate and time. DayCent has not been applied to estimate emissions specific to 2017 and 2019 so it is not clear if the model would underestimate the values for these years although this may be the case given the historical data from 2011 to 2015. Fu et al. (2017) reported emissions of 3.00-4.38 nmol m −2 s −1 during June 1-20, 2010 for the Corn Belt, which is significantly higher than our estimates for June/July 2019. Griffis et al. (2013) estimated the Corn Belt emissions to be around 2 and 1 nmol m −2 s −1 in June/July 2010 and 2011, respectively, which is consistent with our findings. Kort et al. (2008) and Miller et al. (2012) derived scaling factors for the central U.S. To be able to compare their results to ours, we estimated the corresponding flux densities for the Midwest region using their scaling factors for the respective EDGAR versions. Kort et al. (2008) Miller et al. (2012) stated that maximum emissions occurred in June. Our DayCent calculations are also highest in June. This could partly explain our lower estimates compared to Fu et al. (2017) as we report for the end of June/beginning of July after the expected emission peak. Moreover, Fu et al. (2017) only scaled Corn Belt emissions and kept other regions unmodified which could lead to higher estimates, if they sampled other regions with lower emission rates than the Corn Belt. Overall, our estimates are in the range of previous top-down studies. However, the spread among the studies is large.
The nature of soil N 2 O fluxes leads to significant temporal variability in the emissions that is not represented in EDGAR. DayCent is capable of representing those variations to a certain extent. For instance, precipitation events may enhance N 2 O soil emissions (Butterbach-Bahl et al., 2013). DayCent has the potential to simulate such events since it considers meteorology. In October 2017 and June/July 2019, Midwest precipitation amounts were above-average, which probably enhanced N 2 O emissions (see SI and NOAA, 2020a). Especially in 2019, weather conditions in the study domain were unusually extreme. During the campaign, the U.S. was experiencing its wettest period in 125 years, with severe flooding in the Midwest (NOAA, 2020b) forcing the farmers to significantly delay planting in the affected regions (USDA, 2020) and postponing the peak emission period. Depending on whether the zenith is shifted closer to or further away from our investigated period this event may have either amplified or lowered our emission estimates. Additionally, the above-average humidity might have enhanced soil N 2 O emissions leading to higher estimates (Butterbach-Bahl et al., 2013). As indirect N 2 O emissions play an important role in the Midwest (Griffis et al., 2013Turner et al., 2015), flooding-induced emissions pulses of indirect emissions from streams and rivers probably also boosted soil N 2 O fluxes (see SI). The influence of this flooding event cannot be quantified within this study, as this would require more data over longer periods spanning the whole event. However, in a follow-up study we plan to use DayCent simulations driven with those flooding conditions to gain insights on how soil N 2 O emissions were affected.

Conclusion
Unique continuous in-situ airborne N 2 O measurements of 10 research flights were used to quantify N 2 O emissions in the U.S. Midwest using a top-down approach. In October 2017, average emissions were 0.42 nmol m −2 s −1 . The agricultural portion was on average 6.3 times higher than in EDGAR4.3.2 and 3.5 times higher than in EDGAR5.0. June/July 2019 emissions were on average 1.06 nmol m −2 s −1 . For that, agricultural EDGAR4.3.2 fluxes have to be scaled by an average factor of 11.4. EDGAR5.0 performs better again, but still requires an agricultural scaling factor of 9.9. Uncertainties were on the order of 50 %. Our 2019 estimates were most likely influenced by an extreme flooding event, which is difficult to capture in EDGAR as the inventory uses a climatological average emissions data set. Agricultural soil emissions estimated with DayCent in 2011-2015 were 0.32-0.48, 0.16-0.30, and 0.08-0.11 nmol m −2 s −1 in June, July, and October, respectively. These historical emission estimates are higher than nonoptimized EDGAR emissions, but still significantly lower than our optimized fluxes. Our findings are in the range of previous top-down estimates for the Corn Belt and central U.S. However, a quantitative comparison of those studies shows that the range of derived N 2 O surface fluxes is large, likely due to the temporal complexity of N 2 O soil emissions.
More studies focusing on N 2 O are necessary to fully understand the drivers of Midwest N 2 O emissions and the most appropriate modeling methods to estimate emission patterns. To cover the high temporal variability on various scales, long-term projects with regular airborne measurements spanning wide areas of the Midwest are necessary. Combining a process-based model like DayCent capable of simulating the temporal and spatial variability of N 2 O emissions, with extensive airborne and tall tower top-down studies at selected spots and times, could be a cost-effective approach that would limit the number of flights needed to produce accurate estimates for the region and improve national reporting of emissions . As interest grows in expanding efforts to reduce N 2 O emissions (Kanter et al., 2020), improved quantification of N 2 O surface fluxes is mandatory for policy makers to be able to develop effective mitigation strategies.

Data Availability Statement
All ACT-America flask and in situ data used in this manuscript can be found online (at https://daac.ornl. gov/cgi-bin/dataset_lister.pl?p=37 and https://act-america.larc.nasa.gov/).

Acknowledgments
The ACT-America project is a NASA Earth Venture Suborbital-2 project funded by NASA's Earth Science Division (grant NNX15AG76G to the Pennsylvania State University). The authors thank DLR VO-R for funding the young investigator research group "Greenhouse Gases". This work used resources of the Deutsches Klimarechenzentrum (DKRZ) granted by its Scientific Steering Committee (WLA) under project ID bd1104. We also acknowledge funding from BMBF (German Federal Ministry of Education and Research) under project "AIRSPACE" (grant-no. FKZ01LK170). Open access funding enabled and organized by Projekt DEAL.