In the present study, we used the same dataset which was previously published by Acharja et al. (2020, 2021), which described the aerosol time series and chemistry measured with a Monitor for AeRosols and Gases in Ambient Air, model 2S instrument (MARGA). The MARGA system has two channels, one for sampling PM1 and the other for sampling PM2.5 for ground-based observations. The MARGA system (two sampling boxes, analytical box, and connected pumps) was located inside Indira Gandhi International Airport (IGIA), Delhi (28.56∘ N, 77.09∘ E), with the inlet PM1 and PM2.5 impactors fixed on the terrace with 2 m long inlet lines sampling outdoor air at 8 m above ground and 2 m above the rooftop. Measurements covered a winter period (19 December 2017 to 21 January 2018) with frequent moderate to dense fog events. Following intake through the PM1 and PM2.5 impactors, the air was passed through two parallel inlet tubes 2 m long and 14 mm inner diameter polytetrafluoroethylene (PTFE) to the PM1 and PM2.5 sampling channels of the MARGA. The air flow rate in each MARGA sampling box is regulated to a volumetric flow of 1 m3 h-1. The measurements are close to being real-time, as two sets of syringes are employed to collect the samples in which a set of syringes collects the sample, and another set sends the collected samples from the previous hour for analysis. Each MARGA sampling system consists of a steam jet aerosol collector (SJAC) and a wet rotating denuder (WRD) for collecting and measuring water-soluble inorganic particulate species and gases in the ambient air. The continuous coating of the WRD by a thin film of absorption solution (10 ppm hydrogen peroxide (H2O2)) allows for the diffusion of gases into the absorption solution. By contrast, the low diffusion velocity of submicron particles restricts the ability of water-soluble aerosols to diffuse into the absorption solution. The absorption solution is continually changed to replace that abstracted for ion chromatography (IC) analysis of the dissolved gases. The air stream, depleted of gases by the WRD, subsequently enters the SJAC, where the steam enhances water-soluble aerosols to grow, allowing for their mechanical capture in a cyclone. The aqueous solutions deriving from two cyclones (for PM1 and PM2.5, respectively) are then supplied to the IC for chemical analysis (Acharja et al., 2020).

Ambient surface concentrations of NH3 along with other trace gases (HCl, nitrous acid (HONO), nitric acid (HNO3), and sulfur dioxide (SO2)) and water-soluble inorganic components of PM1 and PM2.5 (Cl-, nitrate (NO3-), SO42-, NH4+, sodium (Na+), potassium (K+), magnesium (Mg2+), and calcium (Ca2+) were then quantified online by anion and cation chromatography in the analytical box at an hourly resolution. We have only used PM2.5 inorganic water-soluble components and the gaseous measurements (available from both the PM1 and PM2.5 MARGA collection systems). Since NH4+ with the three major anions, Cl-, NO3-, and SO42-, constituted 97.3 % of the total measured ions in PM2.5 (Acharja et al., 2020), we consider these four significant ions in our present study. In contrast, the remaining ionic species (i.e., Na+, K+, Mg2+, and Ca2+) contributed only about 3 % of the total measured ions and were neglected as it would not impact our present study significantly (Acharja et al., 2020). Anions are separated in a Metrosep A Supp 10 (75/4.0) column with sodium carbonate (Na2CO3) and sodium bicarbonate (NaHCO3) (7/8 mmol L-1) eluent, whereas for cation separation, a Metrosep C4 (100/4.0) cation column with 3.2 mmol L-1 HNO3 eluent was used (Acharja et al., 2020). To suppress the eluent background conductivity of anion chromatographs, three ion exchange units were used to ensure that the ion exchange unit is regenerated in each analysis. For this purpose, 1 M phosphoric acid (H3PO4) was used. This was performed to improve the signal-to-noise (S / N) of the anion chromatographs. Details of the MARGA instrument can be found in Makkonen et al. (2012), Thomas et al. (2009), and Twigg et al. (2015).

To ensure the observation's accuracy and check the data's quality, we have followed best practices during the study. The eluents, absorption, and regenerant solutions were prepared with minimum manual intervention. The operational parameters like anion and cation conductivity, SJAC heater temperature, column oven temperature, and airflow were regularly monitored to keep them within the safe limit. In addition to these, before injection of each sample into the anion and cation IC columns, the lithium bromide (LiBr) internal standard solution containing 320 µg L-1 lithium (Li+) and 3680 µg L-1 bromide (Br-) was mixed with each sample to provide calibration of each analysis. This ensures that each analysis is calibrated, and the concentration of gaseous and ionic samples is measured accurately. The PM1 and PM2.5 impactors were typically cleaned fortnightly to remove any material that may have stuck on the surface and inlets of the impactors. The lower detection limits (LODs) of the species monitored by MARGA were mentioned in Acharja et al. (2021). It shows that concentrations of species like Cl-, NO3-, SO42-, NH4+, SO2, and NH3 were always higher than LODs during the winter period. Concentrations of species like Na+, K+, Ca2+, Mg2+, HCl, HONO, and HNO3 were sometimes below LODs, but the fraction of them was less than ∼ 10 % of the total observation period. We have omitted these values and treated them as not available (NA). As the fraction of observational hours is small, and these species contribute much less to the PM1 and PM2.5 mass concentrations, we believe values that are below the LODs would not significantly deviate our results. The quality of the data obtained was then checked using the ion-balance method. As an additional quality check, the ratio of the sum of cations to anions (nano equivalent per cubic meter – neq m-3) was used as an indicator for the viable data. We have checked the cation-to-anion ratio of each hourly sample expressed in units of neq m-3. We only accepted those values near to unity and rejected those not within the 10 % error bar limit. Based on this evaluation method, overall, for the campaign, the ratio was near unity (1.06 for PM1 and 0.96 for PM2.5). Excellent charge balance between anions and cations measured by the system also confirms that there are no significant contamination issues associated with the aerosol measurements. Values in slight excess of unity may indicate the presence of formate and acetate in the aerosol, which MARGA does not measure. Further details on the quality control of MARGA can be found in Acharja et al. (2020).

Hourly NOx measurements were made by the chemiluminescence method, and hourly ozone (O3) measurements were made by the UV photometric method (CPCB, 2011) at the nearest air quality monitoring station (AQMS) of IGIA, operated by the Central Pollution Control Board (CPCB). CPCB follows the United States Environmental Protection Agency (USEPA)-approved AC32M NOx and 42M O3 analyzer manufactured by Environment S.A. India Private Limited. We used 1 h monitored NOx and O3 values in our study. These air quality monitoring stations' quality control and assurance processes were followed as outlined in CPCB (2014, 2020). For data quality of CPCB, we omitted all those observed values which fell below the LOD of the instrument (2 µg m-3 for NOx and 4 µg m-3 for O3) (Technical specifications for CAAQM station, 2019) and above 500 µg m-3 for NOx and 140 µg m-3 for O3 and treated them as NA at a given site. For the NOx and O3 datasets, only a small fraction of data (2 %) were outside the instrument operating ranges specified. This step aims to remove any short-term local influence that the models cannot capture and retain the regional-scale variability because the nearest sites are located in the urban environment. We removed a single spike represented by a change of more than 100 µg m-3 in just 1 h for all the data in CPCB monitoring stations to filter out random fluctuations in the observations. We removed some very high NOx and O3 values that appeared in the time series right after measurement gaps. Meteorological parameters, including air temperature (T), relative humidity (RH), wind speed, and wind direction, were measured with the automatic weather station (AWS) platform on a 20 m flux tower (Ghude et al., 2017). For detailed information on the measurement site and its meteorological parameters, refer to Ali et al. (2019).

To investigate how well a state-of-the-art chemical transport model performs in capturing the diurnal behavior of NH3 and NH4+, we compared observed and model-simulated diurnal profiles of NH3 and NH4+. Figure 1 displays the comparison of diurnal variation (00:00 to 23:00 Indian standard time (IST)) in meteorological parameters (T and RH) at the IGIA site in Delhi (Fig. 1a) along with NH3 and NH4+ averaged over the study period (Fig. 1b) between observations and the model. We adopted diurnal variation in emissions from a recent study by Jena et al. (2021). Note that diurnal variability in the model simulations is primarily controlled by the planetary boundary layer mixing. We first investigated the ability of WRF-Chem to accurately predict the meteorological parameters of RH and T, which are important determinants of the gas-to-aerosol partitioning of (semi-)volatile compounds. As shown in Fig. 1a, simulated T and RH are in reasonable agreement with the observations, with the simulated RH values falling in the range of 50 %–90 %. Overall, it can be seen that the model shows cold and wet bias compared to the observations but shows warm bias (about 2–3 ∘C) and dry bias (about 10 %–12 %) in the afternoon hours. In spite of the small change in the amplitude of the diurnal cycle of RH, the phase characteristics of the diurnal cycle of both T and RH are reasonably well captured by the model. Figure 1b shows that simulated NH3 and NH4+ are very different compared with the MARGA measurements. The model predicts an average NH3 and NH4+ ± 1σ mass loading of 56.7 ± 14.3 and 14.7 ± 4.9 µg m-3, respectively, while MARGA measurements indicate an average NH3 and NH4+ ± 1σ mass loading of 28.2 ± 12.4 and 36.9 ± 15.1 µg m-3, respectively. We find the diurnal variation of gas-phase NH3 is significantly overestimated by the model (normalized mean bias (NMB) = 1.02). Conversely, NH4+ is underestimated by about 60 % (NMB = -0.60). Simulated NH3 concentrations peak between 07:00–09:00 and 22:00–23:00 with bimodal variation, whilst MARGA shows a single peak around 12:00–13:00. Conversely, a nearly flat diurnal profile of NH4+ is predicted by the model, whereas the average MARGA NH4+ concentration maxima and minima were observed during nighttime (16:00–03:00) and daytime (03:00–08:00 and 09:00–16:00), respectively.

We also looked into the average diurnal profile of NOx and NH3 during dense fog events, and the details can be found in the Supplement (Figs. S1 and S2). It is evident that the observed daytime peak of NH3 did not coincide with NOx peaks, suggesting that traffic emissions do not contribute significantly to the observed NH3 rise. The observed correlation between fog water and enhanced NH3 pulses is consistent with what would also be expected from the evaporation of dew (Sutton et al., 1998; Wentworth et al., 2014, 2016) (Fig. S2 in the Supplement) but is not sufficient to identify whether it is the main cause of the daytime increase of NH3. In the future, measurements of the dew water NH4+ and the accumulation of dew water would be ideal for illuminating the contributing processes. The daytime increase in NH3 concentration could be associated with NH4+ aerosol volatilization driven by an associated sharp change in T and RH (∼ 11:00–12:00) (Sutton et al., 2009a, 2013) off-ground surfaces. The fastest increase in T is 12:00, which is indeed when NH3 was at maximum concentration, indicating that gas-to-particle partitioning may impact the diurnal behavior of NH3 at Delhi during winter (Sutton et al., 2009a, b). However, in the model, because the largest increase in simulated NH3 also precedes the large changes in simulated meteorological parameters, and because the simulated particulate NH4+ is flat compared to observations, simulated meteorology is ruled out as a significant contribution to high bias in simulated NH3. Also, the current model does not include the bidirectional exchange of NH3 with surfaces such as dew and fog water.

To assess the validity of the model, the ratio between simulated and observed (model / obs) was tested. Figure 2 displays the model / obs ratio of daily mean variations in the NH3, NH4+, and total NHx concentrations. The model shows large differences in NH3 and NH4+ compared with observations. We find a model / obs higher than 1 (1.5–4.5) in simulated NH3, indicating the model is biased high (NMB = 1.02), while there is a poor agreement for NH4+ (model / obs less than 0.5), indicating the model is biased low (NMB = -0.62). There is good agreement between the modeled total NHx, which is mostly consistent with the observation (model / obs close to 1) with a small bias (NMB = 0.08). Despite the adequate ability of the model to reproduce the accurate total NHx, the model is biased low for NH4+ and high for NH3, indicating that the model's representation of the gas-to-particle partitioning is not correct. It is, therefore, necessary to understand missing chemical processes in gas-to-particle partitioning responsible for the overestimation of NH3 and underestimation of NH4+ in the model.

Here, diurnal variations of monitored aerosol compounds and gases were analyzed to investigate the gas-to-particle conversion of NH3 in the model. We analyzed the simulation results of the 3 × base HCl run. The diurnal variations for NH3 and NH4+ are controlled mainly by thermodynamic gas-to-particle partitioning, boundary layer mixing, and emission and deposition processes, along with vertical and horizontal advection (Meng et al., 2018). Figure 8 (top) presents the diurnal variations of NH3 and NH4+ (in µg m-3), along with particulate NH4+, Cl-, NO3-, SO42, SO2, HCl, and HNO3 concentrations (in µeq m-3) measured (Fig. 8a (top)) and modeled (Fig. 8b (top)), along with meteorological parameters such as T and RH (Fig. 8 (bottom)). We adopted diurnal variation in emissions from Jena et al. (2021) based on boundary layer mixing. It can be seen in Fig. 8a (top and bottom) that a much bigger peak in NH3 concentration is observed in the daytime than is modeled (despite turbulence differences), indeed suggesting a much stronger NH3 in the middle of the day (11:00–13:00). As evaporation proceeds mainly in the morning (08:00–12:00), getting warmer, the peak is near midday (11:00–13:00), rather than in the afternoon (13:00–14:00), when warmest, similar to what was also observed in Sutton et al. (1998). Indeed, the decreasing NH4+ and Cl- during the late morning (10:00) correspond to the increasing NH3 peak, which reflects the fact that warming promotes the shift of aerosols to the gas phase. Ammonium decreases more than NH3 during the day, as this also evaporates to form NH3. Similarly, Cl- evaporates during the day since the HCl concentration increases. However, it can be seen that NO3- and SO42- are slightly changed diurnally, inferring longer-range transport perhaps, whereas HCl and Cl-are from more local sources. The diurnal variability in gases and aerosols in 3 × base HCl simulations in Fig. 8b (top) is primarily controlled by the planetary boundary layer mixing, meteorology/dispersion, environment (T and RH in Fig. 8b (bottom)), and transport. So presumably, maximum NH3 at 08:00 is due to limited turbulence/boundary layer, with dilution by mixing after 08:00. However, the model is able to represent the diurnal variation of NH4+ and Cl- well, both in terms of amount and pattern, which was not the case in the no HCl run, where NH4+ was observed to be flat in Sect. 1. During the hours of 09:00 and 11:00, when measured NH3 rises, the model predicts a large decrease in NH3, while during 19:00–23:00, when measured NH3 decreases, the model predicts a large increase. Furthermore, the modeled HCl and HNO3 are very low compared to the measurements, whereas SO2 concentration matches well with the observations. It can be seen that NO3- and SO42- are flat in the model. This highlights the need to develop accurate diurnal variability in NH3 emissions over this region.

Figure 9 presents the differences in diurnal variation of mean NH3 (Fig. 9a), NH4+ (Fig. 9b), and total NHx (Fig. 9c) concentration for the three sensitivity experiments. While the simulated NH3 concentrations decrease in the 3 × base HCl compared to the no HCl and base case HCl run (Table 2), none of the model experiments capture the diurnal cycle of NH3. Higher levels of observed NH3 during daytime and modeled NH3 during nighttime highlight the need to improve diurnal variability in NH3 emissions over this region based on the nature and strength of the actual sources. Between the no HCl and the 3 × base HCl run, the NMB for NH3 reduced from 1.38 to 1.13, and NMB for NH4+ systematically improved from -0.61 to -0.03. In contrast, NMB for total NHx increased from 0.12 to 0.39. Table 3 summarizes the statistical indicators for the three sensitivity experiments. An increase in HCl emissions in the 3 × base HCl leads to a higher mass concentration of NH4+ and Cl-, which also increases total mean NHx concentration by 22.4 µg m-3, presumably reflecting the longer atmospheric lifetime of NH4+ compared with NH3. We find consistent high bias in all the simulations for NH3, which is highest during the early morning and at nighttime. In order to better understand the relationship between NH3, NH4+, and NHx concentrations in the diurnal profile of model, one sensitivity study is conducted in the best case HCl experiment to simulate the response of NHx concentrations by changing NH3 emissions. In these simulations, only NH3 emissions were reduced further by a factor of 3 (-3 × NH3_EMI) in the 3 × base HCl experiment, while all other processes and chemical schemes were unchanged. Figure S6 in the Supplement shows the diel profile of model / obs ratio for NH3 (Fig. S6a), NH4+ (Fig. S6b), and total NHx (Fig. S6c) concentration simulated with the 3 × base HCl and -3 × NH3_EMI scenario. Reducing NH3 emissions in the model (-3 × NH3_EMI) significantly improves model–measurement agreement for NH3 (mean model / obs = 1.9), NH4+ (mean model / obs = 0.9), and total NHx concentration(mean model / obs = 1.2) compared to the 3 × base HCl run, further suggesting that the longer lifetime of NH4+ may be the controlling driver for the total NHx concentration in the model.

Figure S7 in the Supplement illustrates a time-series graph that compares daily mean NH3 (Fig. S7a), NH4+ (Fig. S7b), and total NHx concentrations (Fig. S7c) for the three sensitivity experiments, and Table 2 shows the mean ± 1σ of these variables. The results show that compared to the no HCl run, NH3 mean concentrations decreased by 2 µg m-3 in the base case HCl and decreased by a further 3.2 µg m-3 in the 3 × base HCl run. Conversely, NH4+ mean concentration increases in the base case HCl by 7.5 µg m-3 and further increases by 13.1 µg m-3 (3 × base HCl). This decrease in NH3 is associated with the enhanced gas-to-particle conversion of NH3 to NH4+. Associated with these changes, total mean NHx also increased by 5.5 and 9.8 µg m-3 in the base case HCl and 3 × base HCl, respectively, compared to the no HCl. This is likely due to associated increases in the atmospheric lifetime of NHx with respect to deposition as the partitioning shifted from the faster depositing gas phase to the aerosol phase. The lifetime of NH3 is very short, a few hours, while that of NH4+ is 1 to 15 d (Aneja et al., 1998; Nair and Yu, 2020; Pawar et al., 2021; Q. Wang et al., 2020).

To understand the overestimation of total NHx in the daily mean variation by the model further, we compared the 3 × base HCl and -3 × NH3_EMI sensitivity experiment. Figure 10 shows the ratio of model / obs for NH3 (Fig. 10a), NH4+ (Fig. 10b), and total NHx (Fig. 10c) concentration. It can be seen that the model–measurement agreement improves significantly (model / obs closer to 1) after reducing NH3 emissions for all three metrics. The -3 × NH3_EMI run would reduce the mean NH3, NH4+, and total NHx concentration by ∼ 8.1, 3.2, and 11.3 µg m-3, respectively, compared to the 3 × base HCl run. Even though NH3 emissions are reduced, they are still sufficient to react rapidly with the varying HCl in the sensitivity experiments, contributing to an increase in NH4+. As can be seen in Fig. 10b, initially, NH4+ is somewhat lower, but it increases later and matches the 3 × base HCl run. This suggests that NH4+ formation in the model is more sensitive to changes in HCl than changes in NH3 emission, while total NHx agrees well by reducing the NH3 emissions. In general, CTMs have higher NH3 concentration than observations, further supporting models having too much NH3. A few factors might contribute to the model discrepancies for NH3: there are uncertainties in the emission inventory of the bottom-up approach of NH3, and the model does not currently include the bidirectional exchange of NH3 with surfaces, such as dew and fog water. Also, the model does not have accurate industrial sources of HCl emission. Diurnal emission profiles are uncertain for both NH3 and HCl. Furthermore, gas-to-particle partitioning associated with SO2 oxidation pathways in the model is not correct at present.