The STAGE deposition option closely follows the widely used Massad et al. (2010) and Nemitz et al. (2001) parameterizations, modified to include the option for a cuticular compensation point and is unique in CMAQ as it employs the same resistance model for bidirectional and unidirectional exchange (Fig. 1).

The flux of a trace gas between the atmosphere and surface is modeled following Nemitz et al. (2001) as: 1Ft=-Ca-Cz0Ra where, Ca is the ambient atmospheric concentration, Cz0 is the compensation point concentration at the sum of the aerodynamic displacement height (d) and roughness length (z0) and Ra is the aerodynamic resistance. The compensation point is estimated using a two-layer, soil and canopy model following Nemitz et al. (2001). 2cz0=CaRa+ClRb,v+CgRgndRa-1+Rb,v-1+Rgnd-1 Cl is the compensation point at the leaf, Cg is the soil air-pore space concentration, Rb,v is the leaf quasi-laminar boundary layer resistance following Massad et al. (2010), and Rgnd is defined as the sum of the in-canopy resistance, soil quasi-boundary layer resistance and soil resistance (Rgnd=Rinc+Rb,s+Rsoil). Cl is estimated by solving for the exchange between the canopy compensation point and the atmosphere, stomata, cuticle and ground following Kirchhoff's current law (see Nemitz et al., 2000). Cl is solved from this system of equations following the work of Nemitz et al. (2001) with the addition of a cuticular compensation point: 3Cl=CaRaRb,v+CstomRaRs+Rb,vRs+RgmdRs+CcutRaRcut+Rb,vRcut+RgndRcut+CgRb,vRgndRaRb,v-1+RaRs-1+RaRcut-1+Rb,vRs-1+Rb,vRcut-1+Rb,vRgnd-1+RgndRs-1+RgndRcut-1 where, Cstom is the gaseous compensation point concentration in the leaf mesophyll, Ccut is the gaseous compensation point concentration at the cuticular surface, Rs is the sum of stomatal and mesophyll resistances, and Rcut is the cuticular resistance. The resistance parameterization algorithms and references are listed in Table 1.

The cuticular and soil pathways can be either dry, wet or snow covered where each pathway is assumed to be parallel. 4Rx=fdryRx,dry+fwetRwet+fsnowRsnow where Rx is either the cuticular or soil resistance, fdry, fwet and fsnow are the ratio of dry, wet or snow covered surface to the surface area constrained by fdry+fwet+fsnow=1, Rx,dry is the resistance of the modeled species to dry soil or cuticular surfaces, Rwet is the resistance of the modeled species to deposition to surface bound water droplets, and Rsnow is the resistance of the model species to deposition to snow covered surfaces.

If the soil, cuticular and stomatal compensation points are zero, then the transfer coefficient in this resistance model reduces to a typical dry deposition model similar in form to Clifton et al. (2020): 5Vd=Ra+11Rb,v+11Rcut+1Rs+1Rgnd-1 where Vd is the dry deposition velocity and the flux can be modeled as: 6Ft=-CaVd

This allows for the use of this resistance model framework for species that exhibit bidirectional exchange, e.g., NH₃, and species that do not, e.g., HNO₃, and has the advantage of having a consistent set of assumptions regarding the deposition and bidirectional exchange of pollutants. Similarly, the evasive portion of the flux in the CMAQ implementation is estimated following Bash et al. (2013) to separate evasive and deposition fluxes. 7Ft=-CaVd+Cz0Ca=0.0Ra

Splitting deposition and emission processes allows for the application of source apportionment tools to species that exhibit bidirectional exchange and estimate emission sensitivities, e.g., the sensitivity of ambient NH₃ to agricultural fertilizer applications.

Several updates were made to the soil processes in the NH₃ bidirectional exchange algorithms for the STAGE deposition option implementation in CMAQ v5.3.2. The first was specifying a maximum diffusive length in estimating the resistance to emissions or deposition to soil surfaces. Earlier versions of CMAQ used the 1 cm soil layer depth of the P-X land surface model (Pleim and Xui, 1995). This was changed to 2 cm to be consistent with the measurements used to derive the diffusive model (Kondo et al., 1990) and to fall in the middle of the dry layer thickness range of 1 to 3 cm reported by Swenson and Lawrence (2014).

Releases of CMAQ before v5.3 estimated that 55 % of the soil ammonium was in the soil water solution based on measurements with extractants with variable ionic strengths (Cooter et al., 2010). Here, we employ the non-linear ammonium sorption capacities to estimate the NH4+ in the soil water solution and available for evasion (Venterea et al., 2015). 18NH4,s+=μNH4,aq+K+NH4,aq+ where NH4,s+ is the ammonium sorbed to soil particles, NH4,aq+ is the ammonium in the soil water solution, μ is the maximum soil sorption capacity and K is the NH4,aq+ concentration where NH4,s+=0.5μ (Table 2).

Field-scale flux data collected from 5 July to 23 November 2012 at a managed, unfertilized 15 ha grass field at the Duke Forest Blackwood Division, NC (35.58° N, 79.05° W; Rumsey and Walker, 2016) from 5 July to 23 November 2012 and at a 200 ha fertilized corn field near Lillington, NC (35.38, 78.78° N; Walker et al., 2013) from 29 May to 29 June 2007 were used to evaluate the STAGE model. Micrometeorological flux measurements of NH₃ and latent heat available at both sites and HNO₃ and SO₂ fluxes are available at the Duke Forest site were used to evaluate modeled fluxes. At Lillington, air concentrations and above-canopy vertical gradients of NH₃ were measured with a continuous flow “AMANDA” (Ammonia Measurement by ANnular Denuder sampling with online Analysis; Wyers et al., 1993) wet denuder system and fluxes were determined using the modified Bowen ratio method (Meyers et al., 1996). At Duke Forest, air concentrations and above-canopy vertical gradients of HNO₃, SO₂ and NH₃ were measured using the Monitor for AeRosols and GAses in ambient air (MARGA, Metrohm-Applikon, the Netherlands) (Rumsey et al., 2014) and fluxes were determined using the aerodynamic gradient methods (Thomas et al., 2009). At both sites, eddy covariance was used to determine fluxes of latent heat using an open-path infrared gas analyzer (LI-COR 7500, LI-COR, Inc., Lincoln Nebraska). LAI was not measured during the flux campaign at Duke Forest but there were measurements of canopy height and LAI (LAI-2000, LI-COR, Inc., Lincoln, Nebraska) during other periods. This data was used to estimate LAI as a function of canopy height. In the spring and summer, it was assumed LAI =3.25Hc and in the fall this relationship was assumed to be LAI =1.35Hc due to the drying of the canopy and senescence. Methods for biogeochemical measurements and compensation points for Duke Forest are included in the supplemental material and are described by Walker et al. (2013) for Lillington.

A field-scale box model was developed in the R statistical language that utilizes the same resistance parameterizations and structure as the CMAQ FORTRAN model (see supplemental material). Observed soil and vegetation NH₃ compensation points were set as the median values reported in Walker et al. (2013) and measured at Duke Forest (see supplemental material) and using CMAQ model parameterized values. Latent heat fluxes were estimated by specifying a water vapor stomatal and soil compensation points assuming saturation at the measured leaf and soil temperatures. Fluxes of HNO₃ and SO₂ utilized the same modeling framework with compensation points set to zero for all surface media.

The field-scale model was run for two field campaigns to evaluate its performance in capturing NH₃ and H₂O bidirectional exchange at agricultural and grassland sites and to evaluate its performance in capturing HNO₃ and SO₂ exchange at a grassland site. These simulations utilized the resistance parameterizations indicated here with the exception of the aerodynamic resistance, which was defined as Ra=Pr0U‾u*2, where Pr₀ is the turbulent Prandtle number (assumed to be 0.95). Note, this results in a similar parameteization of Ra as Pleim and Ran 2011, Table 1, if U‾ is estiamted from u* assuming a log linear wind profile. Latent heat fluxes were estimated by assuming that the leaf and soil H₂O compensation points are the saturation vapor pressure at the canopy and soil temperatures, respectively. A sensitivity simulation was conducted for both field scale sites to assess the sensitivity of the STAGE parameter uncertainty. This sensitivity simulation consisted of perturbing the CMAQ v5.3.2 default minimum stomatal resistance, cuticular resistance, and ground resistance by ±50 %.

The model developed by Massad et al. (2010) and Nemitz et al. (2001) with the modifications above is designed to be applied to specific land use types. In the CMAQ v5.3.2 application, this is accomplished by estimating a deposition velocity for each land use type in a grid cell and calculating the grid cell total as an area weighted sum. 19Ft,grid=∑LU=1NLUfLUFt,LU where, Ft,grid is the grid scale flux, LU is the land use index, NLU is the number of land uses in the grid cell, fLU is the ratio of the land use area to total grid area, and Ft,LU is the land use specific flux. This scheme makes it necessary to estimate land use specific resistances. This is currently accomplished by applying the land use specific surface roughness length, minimum stomatal resistance, and leaf area index values from the P-X land surface model (Pleim and Xiu, 1995) look up tables in the WRF v4.1.1 model (Skamarock et al., 2019) to recalculate the surface friction velocity and stomatal resistance.

Multiple CMAQ model simulations for the year 2016 were used in this evaluation. Meteorological inputs were from a WRF v4.1.1 simulation using the P-X land surface model, FEST-C model simulations (Ran et al., 2019) were used to provide agricultural data to support the bidirectional exchange model, and emissions were based on the 2016 EMP (Emissions Modeling Platform: https://www.epa.gov/air-emissions-modeling/2014-2016-version-7-air-emissions-modeling-platforms, last access: 15 September 2026, Appel et al., 2021) . Additional details regarding the model simulations and CMAQ v5.3.2 model performance with the STAGE deposition option can be found in Appel et al. (2021). In this study, we explore the ammonia bidirectional exchange results and conduct model sensitivities that incorporate observed fertilization rates and observed values for non-agricultural leaf and soil Γ to evaluate the model sensitivity to these factors.

FEST-C model simulations are known to under-estimate annual fertilization rates (Ran et al., 2019). To explore how this model bias impacts CMAQ v5.3.2 ambient NH₃ concentrations and deposition estimates, USDA Economic Research Services (ERS) reported annual fertilizer data was used to post-process FEST-C output for corn, cotton, soybean, and wheat. EPIC fertilizer rates were adjusted by multiplying the grid cell fertilization rate by the ratio of the USDA ERS reported rate over the average FEST-C rate for the state and crop. For states that did not have reported values, the mean ratio of the USDA ERS rate over the mean FEST-C rate for states that had data was used for the adjustment (Eq. 20). The mean adjustment factor for nitrogen fixing crops, soybeans in this case, and non-nitrogen fixing crops were used to adjust the fertilization rate of these crops respectively. 20Fertadjusted,crop=maxFertsubmitted,crop1ncrop∑FertFEST-C,cropFertFEST-C,crop,Fertmax,crop where Fert_{adjusted,crop} is the FEST-C grid cell adjusted fertilization rate, Fert_Submitted,i is the USDA mean annual application data for the specified crop, in kg ha⁻¹, Fert_FEST-C,crop is the initial FEST-C grid cell fertilization rate for the state being considered, ncrop is the number of grid cells with fertilization use for the specified crop in the state, and Fert_max,crop is the maximum fertilization rate estimated from EPIC for the crop, typically about 300 kg ha⁻¹ for a non-nitrogen fixing crop. Nitrification and mineralization rates are captured from FEST-C and evasion rates are estimated using the resistance model above to calculate the nitrogen balance for the modeled soil layers.

At the field scale, hourly modeled fluxes are compared to micrometeorological observations from a fertilized Zea mays field and an unfertilized managed grass field. Mean and median modeled values are evaluated against observations over the complete measurement period for configurations of the box model using parameterizations from the STAGE model in CMAQ v5.3.2 and using observed values (Table 3). The following model cases were simulated to evaluate the default CMAQ v5.3.2 values for the agricultural Lillington, NC and grassland Duke Forest, NC sites.

LM – STAGE model simulation of Lillington, NC fluxes using the default CMAQ v5.3.2 tabular inputs.

Evaluation of regional scale results of this model against network observations has been published elsewhere (Appel et al., 2021). Here we focus on the evaluation of the regional scale model estimates against Cross-Track Infrared Sounder (CrIS) satellite observations, Shephard et al. (2020), and estimate the agricultural nitrogen budget and its sensitivity to the parameterization of the NH₃ emission potential.

The STAGE model captured the observed diel variability and magnitude of the HNO₃ and SO₂ fluxes well (Fig. 1 and Table 3). The H₂O fluxes at Lillington, NC (LO H₂O) and Duke Forest, NC (DM H₂O) were overestimated by 27.0 % and 38.6 % when modeled with the available site-specific data, respectively, Table 3. The error in the Lillington, NC H₂O flux is near the high end of estimated error in eddy covariances fluxes reported by Rannik et al. (2016). The evaluation of modeled H₂O and NH₃ fluxes at Duke Forest had higher error than those at the Lillington site (Table 3). This is likely influenced by uncertainty introduced by the lower magnitude of the measured fluxes at the Duke Forest site and the lack of LAI and minimum stomatal resistance measurements which govern the cuticular and stomatal exchange processes respectively. The normalized mean bias of the NH₃ flux at the Duke Forest site of all the model cases, Table 3, were outside the range of the measurement uncertainty of 31 % reported by Rumsey and Walker (2016). However, the DFOS and DFOL cases using observed emission potentials, Table 2, resulted in a reduction of the model biases of the estimated NH₃ flux with a substantial increase in the correlation over the DFM case. The DFM case underestimated the observed flux and estimated net deposition over the measurement period. The model was better able to capture the net flux when the observed emission potentials were used in the DFOS and DFOL cases resulting in a higher model correlation. In general, the median modeled NH₃ fluxes generally underestimated the observed median (Table 3). The diel fluxes indicate that model underestimated nighttime and early morning NH₃ evasive fluxes and captured midday and afternoon fluxes well (Fig. 2b). Sensitivity simulations identified that NH₃ emission potentials for the stomata and ground (represented by leaf litter or soil) can largely explain the biases in the modeled fluxes (Table 3). These measured compensation points are larger than the values parameterized in Massad et al. (2010) used in CMAQ v5.3.2, Table 2, and model results using these values at the duke forest site resulted in an averaged -1.3 ng m⁻² h⁻¹ deposition flux while the observed flux was a net emission for the measurement period (Table 3). Model sensitivities at this site show that the modeled fluxes are most sensitive to Γ_apoplast and our measurements of Γ_apoplast at this site are similar in magnitude to other studies (e.g. Wang and Schjoerring, 2012; Wichink Kruit et al., 2007).

The STAGE model captured the magnitude and variability of the observed values at the fertilized corn canopy measured during the Lillington, NC flux campaign with a normalized mean bias of -23.4 % when using the median value for the soil NH4+ and pH, 31 689.7 µM and 6.43, respectively, and a Γ_apoplast of 153.5 reported by Walker et al. (2013) and 40.5 % when using the CMAQ v5.3.2 parameterizations (Table 3 and Fig. 3). As noted in Walker et al. (2013), the Γ_apoplast measurements at this site are much lower than values inferred from micrometeorological measurements, and this may be due to the extraction technique used and/or the growth stage of the crop during which the apoplast chemistry was measured. The modeled NH₃ flux at these sites is most sensitive to the soil and vegetation emission potentials and the model estimates bound both the Lillington and Duke Forest, NC measurements if the median or mean of measured soil emission potentials reported in Walker et al. (2013) and measured at Duke Forest are used.

A consistent min morning emission peak was observed at the Lillington, NC site (Walker et al., 2013). The emissions appear to be related to the drying of the canopy in the morning and similar morning emissions have been observed for a grass canopy (Wentworth et al., 2014). A high emission potential was measured on the dew present on the leaves in the morning (Table 2). When the dew compensation point was included in the STAGE model, case LO, there was insufficient ammonium in the dew to explain the emission peak, Fig. S1, in agreement with Walker et al. (2013). At the Lillington site, the canopy did not contain dew according to the leaf wetness measurements after 08:00 EST, Fig. S2, and the modeled evasion from dew occurred before this period while the observed morning evasion occurred primarily between 08:00 and 11:00 EST when the canopy was dry (Fig. 3). The soil between plants and rows at the Lillington site was exposed and had a much higher emission potential than the canopy. We speculate that the mid-morning emission peak could be due to the wetting and drying of soil surfaces rich in NH4+ that was not captured by the soil moisture probes. These results are in contrast to the dew drying experiments of Wentworth et al. (2014), where they estimated that the evasion of NH₃ during morning dew evaporation could account for morning increases in NH₃ at a high elevation grassland field site at Rock Mountain National Park, CO.

The field scale simulations of the Lillington, NC and Duke Forest, NC observations indicate that the STAGE deposition model captures the observed SO₂, HNO₃, and NH₃ fluxes well when measured soil and canopy parameters are used (Table 3). However, when CMAQ v5.3.2 tabular data are used in the simulation the STAGE model fails to capture the magnitude or even the direction of the observed NH₃ flux at the Duke Forest site. At the Duke Forest site, the sensitivity simulations perturbing the minimum stomatal resistance, cuticular resistance, and ground resistance were unable to capture the direction of the mean observed NH₃ flux and generally increased the biases of the modeled SO₂ flux (Table S1). The modeled HNO₃ flux is generally insensitive to the canopy resistance parameters as it is primarily governed by the aerodynamic resistance (Table S1). At the Lillington site, the modeled NH₃ flux is sensitive to both the emission potential and the ground resistance indicating the importance of accurately characterizing soils in fertilized agricultural sites for estimating NH₃ fluxes (Table S1). This is the first evaluation of the CMAQ bidirectional NH₃ exchange parameterization against non-agricultural flux observations and indicates that the tabular data in CMAQ v5.3.2 do not reflect the ammonia emission potentials at the Duke Forest, NC field site. The model evaluation at the Lillington, NC agricultural is comparable to previous studies (Pleim et al., 2013). Additional measurements of soil and vegetation, NH4+, pH, and NH₃ emission potentials would be beneficial in improving CMAQ model emissions and deposition estimates in non-agricultural regions which accounts for approximately 75 % of terrestrial surfaces of the 12 km conterminous US model domain.

Annual ambient NH₃ concentration estimates using the CMAQ modeling system generally capture the magnitude and spatial patterns observed in Cross Infrared Sounder (CrIS) v1.6 (Shephard et al., 2020; Shephard and Cady-Pereira, 2015) satellite observations (Fig. 4). CrIS v1.6 has a detection limit of approximately 0.5 ppb under typical atmospheric conditions (Shephard et al., 2025). Here we limited analysis to CrIS observations made during cloud free days and regions where the CrIS observations are generally greater than 1 ppb (Fig. 4a). CMAQ v5.3.2 model concentrations were paired in space and time with the CrIS observations. Model estimates exceed CrIS observations in the agricultural regions of California, the Upper Midwest, and Eastern North Carolina and underestimate observations in the Great Plains, the leeward side of the Sierra Nevada's in the Mojave Desert, Eastern Washington, and the agricultural regions of North Central Mexico and coastal areas of Sinaloa Mexico (Fig. 4). The mean overestimates in these areas range from 0.5 to 0.9 ppb with maximum overestimates from 7.1 to 9.5 ppb, while mean underestimates at these sites range from -0.6 to -0.62 ppb with maximum underestimates from -2.6 to -3.8 ppb. EPIC fertilization estimates used in CMAQ (Cooter et al., 2012; Bash et al., 2013) only cover the conterminous United States, while values in the Canadian and Mexican portions of the domain use look up tables for agriculture following Zhang et al. (2010) which likely contribute to the observed biases between CMAQ and the CrIS retrievals in Mexico. CMAQ underestimates CrIS NH₃ observations by approximately 1 ppb over a large swath of non-agricultural land areas (Fig. 4). The general CMAQ underestimate of CrIS NH₃ observations in these areas indicates that the CMAQ tabular emission potentials for non-agricultural areas may be generally underestimated as they were for the Duke Forest, NC site. The biases on the leeward side of the Sierra Nevada Mountains where there is little vegetation could be due to the evaporation of NH₄NO₃ aerosols which CMAQ underestimates from the intensive agricultural and urban areas upwind (Kelly et al., 2018) as airmasses undergo adiabatic heating. Currently, we lack ambient NH₃ measurements and measurements of soil and vegetation emission potentials in the Mojave Desert or any other desert regions and can only speculate as to the cause of the model underestimation.

Annual regional scale CMAQ model NH₃ values evaluated against CrIS observations show biases that are directionally consistent with the box model simulations over both grasslands and agricultural areas indicting that the default tabular values are contributing to the observed model biases. Additionally, regional scale model results in the agricultural regions of California and Midwestern U.S. overestimate the CrIS observations (Fig. 3). When compared to CrIS and AMoN sites model biases are likely to be reduced with an increase in the natural NH₃ emission potentials for grasslands. Approximately a 30 % increase in the vegetation emission potential and factor a of 5 increase in the soil surface emission potential would better match the observations at the Duke Forest, NC grasslands site, Table 2, and likely improve the evaluation against CrIS observations in the Great Plains. While this would represent a relatively large change from the existing values for Γ in CMAQ, this change is also well within the variability of vegetation and soil Γ measurements (Walker et al., 2013; Zhang et al., 2010; Wentworth et al., 2014).

Regional scale evaluations of trace gas deposition rates and processes are currently limited by sparse flux measurement observations. Ambient air-quality monitoring networks and satellite observations can provide an indirect evaluation of dry and wet deposition processes but are often missing key observations needed to better constrain model processes, e.g. soil and vegetation NH₃ emission potentials Γ, or particulate matter observations to constrain the impact that aerosol-gas partitioning has on ambient concentrations. Due to the lack of co-located NH4+ aerosol observations, our current ability to evaluate NH₃ using satellite and network data are limited to areas where aerosol partitioning processes are likely negligible. Thus, the regional scale CMAQ v5.3.2 evaluation against network (Appel et al., 2021) and CrIS observations best constrain areas that exhibit high NH₃ emissions resulting in high ambient NH₃ concentrations that are less likely to be impacted by modeled errors in NH4+. Additionally, the estimated fluxes can be qualitatively evaluated by examining the nitrogen deposition and emission budget against previously published values. Here we tabulate evasion estimates and compare them to fertilizer estimates using the EPIC model (Ran et al., 2019). For the 2016 simulations of Appel et al. (2021), 10.3 MT of N were estimated to be applied as fertilizer to row crops, of that the bidirectional exchange model in CMAQ estimated that 0.5 MT of N, or 4.8 % annual emission factor, if estimated to be emitted as NH₃ (2017 NEI). An annual NH₃ emission factor for mineral fertilizers of 4.8 % is within the range of reported values of Klimont and Brink (2004). Deposition values peaked downwind of agricultural sources at approximately 30 kg N ha⁻¹ in Eastern North Carolina (Fig. 5), and are well within measured annual deposition values downwind of agricultural sources (Shen et al., 2016) but higher than the net deposition flux of 10 to 16 kg N ha⁻¹ reported by Walker et al. (2014) and Walker et al. (2008) respectively for this region. The CMAQ estimated net NH₃ flux is deposition in this area yet CMAQ NH₃ concentration estimates are approximately two to three time higher than CrIS observations indicating that NH₃ emissions from sources other than bidirectional exchange may be overestimated or CrIS observations are underestimated in Eastern North Carolina.