Semi-quantitative understanding of source contribution to nitrous acid (HONO) based on 1 year of continuous observation at the SORPES station in eastern China

Nitrous acid (HONO), an important precursor of the hydroxyl radical (OH), has long been recognized as of significance to atmospheric chemistry, but its sources are still debated. In this study, we conducted continuous measurement of HONO from November 2017 to November 2018 at the SORPES station in Nanjing of eastern China. The yearly average mixing ratio of observed HONO was 0.69±0.58 ppb, showing a larger contribution to OH relative to ozone with a mean OH production rate of 1.16 ppb h⁻¹. To estimate the effect of combustion emissions of HONO, the emitted ratios of HONO to NO_x were derived from 55 fresh plumes (NO∕NO_x > 0.85), with a mean value of 0.79 %. During the nighttime, the chemistry of HONO was found to depend on RH, and heterogeneous reaction of NO₂ on an aerosol surface was presumably responsible for HONO production. The average nighttime NO₂-to-HONO conversion frequency (C_HONO) was determined to be 0.0055±0.0032 h⁻¹ from 137 HONO formation cases. The missing source of HONO around noontime seemed to be photo-induced, with an average P_unknown of 1.04 ppb h⁻¹, based on a semi-quantitative HONO budget analysis. An over-determined system of equations was applied to obtain the monthly variations in nocturnal HONO sources. Besides the burning-emitted HONO (accounting for about 23 % of the total concentration), the contribution of HONO formed heterogeneously on ground surfaces to measured HONO was an approximately constant proportion of 36 % throughout the year. The soil emission revealed clear seasonal variation and contributed up to 40 % of observed HONO in July and August. A higher propensity for generating HONO on aerosol surfaces occurred in severe hazes (accounting for 40 % of the total concentration in January). Our results highlight ever-changing contributions of HONO sources and encourage more long-term observations to evaluate the contributions from varied sources.

1 Introduction

Nitrous acid (HONO) is a vital constituent of nitrogen cycle in the atmosphere, first observed in the field by Perner and Platt (1979). The concentrations of HONO varied from dozens of parts per trillion in remote regions (Villena et al., 2011b; Meusel et al., 2016) to several ppb in polluted urban regions (Yu et al., 2009; Tong et al., 2015). The photolysis of HONO (R1) has been long standing as a momentous source of the hydroxyl radicals (OH), especially during the early morning, when other OH sources are minor (Platt et al., 1980; Alicke, 2002, 2003). Even during the daytime, recent studies have recognized the photolysis of HONO as a potentially stronger contributor to daytime OH radicals than that of O₃ (Kleffmann, 2005; Elshorbany et al., 2009; Li et al., 2018). Meanwhile, HONO has been found to affect adversely human heath (Jarvis et al., 2005; Sleiman et al., 2010).

Although the significance of HONO has been given much weight, the sources of ambient HONO are complicated and have been debated for decades. HONO can be emitted from combustion, including vehicle exhaust, industrial exhaust and biomass burning (Table 1). Tunnel experiments with tests for different engine types have determined an emission ratio of HONO∕NO_x for traffic sources, ranging from 0.3 % to 0.8 % (Kirchstetter et al., 1996; Kurtenbach et al., 2001). The release from soil nitrite through acidification reaction and partitioning is considered to be another primary source of atmospheric HONO (Su et al., 2011). Soil nitrite can come from biological nitrification and denitrification processes (Canfield et al., 2010; Oswald et al., 2013) or be enriched via reactive uptake of HONO from the atmosphere (VandenBoer et al., 2014a, b). In addition to direct emissions, the vast majority of HONO is produced chemically. The recombination of NO and OH (R3) is the main homogeneous reaction for supplying HONO (Pagsberg et al., 1997; Atkinson, 2000), whose contribution may be significant under conditions of sufficient reactants at daytime. During the nighttime, with low OH concentrations, other larger sources, i.e., heterogeneous reactions of NO₂ on various surfaces, are required to explain elevated mixing levels of HONO. Laboratory studies indicate that NO₂ can be converted to HONO on humid surfaces (Reaction R4), being first order in NO₂ and depending on various parameters including the gas-phase NO₂ concentration, the surface water content, and the surface area density (Kleffmann et al., 1998; Finlayson-Pitts et al., 2003). Besides, the heterogeneous reduction of NO₂ with surface organics (R5) is proposed to be another effective pathway to generate HONO (Ammann et al., 1998, 2005; Aubin and Abbatt, 2007), observed in freshly emitted plumes with high concentrations of NO_x (Xu et al., 2015). Notably this reaction rate is drastically reduced after the first few seconds due to consumption of the reactive surfaces (Kalberer et al., 1999; Kleffmann et al., 1999), but this reaction could be strongly enhanced by light on photo-activated surfaces (George et al., 2005; Stemmler et al., 2006, 2007). During the daytime, heterogeneous HONO formation from the photolysis of adsorbed nitric acid (HNO₃) and particulate nitrate (${\mathrm{NO}}_{\mathrm{3}}^{-}$) at UV wavelengths has been found in experiments and observations (Zhou et al., 2003, 2011; Ye et al., 2016, 2017). Heterogeneous processes are typically considered the main sources of HONO in many regions, yet are the most poorly understood. For NO₂ conversion to HONO on surfaces (R4, R5), the uptake coefficients of NO₂ derived from different experiments vary from 10⁻⁹ to 10⁻² (Ammann et al., 1998; Kirchner et al., 2000; Underwood et al., 2001; Aubin and Abbatt, 2007; Zhou et al., 2015). The key step to determine the uptake of NO₂ or the reaction rate is still ill-defined, and we are also not certain whether and how the ambient natural surfaces can be reactivated by radiation. Furthermore, it has become a main concern to compare the contributions of ground and aerosol surfaces to HONO formation. It is so far not well explained for the observed HONO, especially during daytime. Large unknown sources of HONO have been identified by many studies (Su et al., 2008b; Sörgel et al., 2011; Michoud et al., 2014; Lee et al., 2016).

Table 1 Sources and sinks for HONO in the troposphere.

Benefitting from more and more studies, particularly the observations under different environments (Lammel and Cape, 1996; Li et al., 2012), understanding of HONO chemistry in the atmosphere has been greatly improved during the last decade. However, most HONO observations were short-term campaigns, with studies ranging from several weeks to several months. For example, Reisinger (2000) found a linear correlation between the HONO∕NO₂ ratio and aerosol surface density in the polluted winter atmosphere, Nie et al. (2015) showed the influence of biomass burning plumes on HONO chemistry, according to observed data during late April–June 2012, while Wong et al. (2011) believed that NO₂-to-HONO conversion on the ground was the dominant source of HONO by analyzing vertical profiles from 15 August to 20 September 2006. Moreover, a perspective that HONO from soil emission explained the strength and diurnal variations of the missing source has been presented by Su et al. (2011) based on data measured from 23 to 30 October 2004. In case the HONO sources exhibit temporal variability, especially seasonal differences, it is challenging to draw a full picture on the basis of these short-term observations. More than a year of continuous observation is needed, yet is rather limited.

The Yangtze River delta (YRD) is one of the most developed regions in eastern China. Rapid urbanization and industrialization have induced severe air pollution over the last 3 decades, particularly high concentrations of reactive nitrogen (Richter et al., 2005; Rohde and Muller, 2015), including HONO (Wang et al., 2013; Nie et al., 2015). In this study, we conducted HONO observations continuously from November 2017 to November 2018 at the Station for Observing Regional Processes and the Earth System (SORPES) located in the western part of the YRD, a place that can be influenced by air masses from different source regions of anthropogenic emissions, biomass burning, dust and biogenic emissions (Ding et al., 2013, 2016). Our 1-year observation showed well-defined diurnal patterns and obvious seasonal variations of HONO concentrations at relatively high levels. We discussed the potential mechanism of HONO production based upon semiquantitative analysis and correlation studies and paid special attention to changes in major sources of HONO during different seasons.

2 Methodology

2.1 Study site and instrumentation

Continuous observation was conducted at the SORPES station at the Xianlin Campus of Nanjing University (118^∘57^′ E, 32^∘07^′ N), located in the northeastern suburb of Nanjing, China, from November 2017 to November 2018 (Supplement Fig. S1). The easterly prevailing wind and synoptic condition make it a representative background site of Nanjing and a regional downwind site of the city cluster in the YRD region. Detailed descriptions for the station can be found in previous studies (Ding et al., 2013, 2016).

HONO was measured with a commercial long-path absorption photometer instrument (QUMA, model LOPAP-03). The ambient air was sampled in two similar temperature-controlled stripping coils in series using a mixture reagent of 100 g sulfanilamide and 1 L HCl (37 % volume fraction) in 9 L pure water. In the first stripping coil, all of the HONO and a fraction of interfering substances were absorbed into solution, and the remaining interfering species (NO₂, HNO₃, HO₂NO₂, PAN, etc.) were absorbed in the second stripping coil. After adding a reagent of 0.8 g N-naphtylethylendiamine-dihydrochloride in 8 L pure water, colored azo dye was formed in the solutions from two stripping coils, which were then separately detected via long-path absorption in special Teflon tubing. To minimize the measurement interferences, the real HONO signal was the difference between the signals in the two channels. Further details can be found in Heland et al. (2001) and Kleffmann et al. (2006). To correct for the small drifts in the instrument's baseline, the compressed air was sampled every 12 h (flow rate: 1.0 L min⁻¹) to make zero measurement. A span check was made using 0.04 mg m⁻³ nitrite (${\mathrm{NO}}_{\mathrm{2}}^{-}$) solution every 2 weeks with a flow rate of 0.28 mL min⁻¹. The time resolution, detection limit, and accuracy of the measurement were 5 min, 10 pptv, and 10 %, respectively.

The NO and NO₂ levels were measured using a chemiluminescence instrument (TEI, model 42i) coupled with a highly selective photolytic converter (Droplet Measurement Technologies, model BLC), and the analyzer had a detection limit of 50 pptv for an integration time of 5 min, with precision of 4 % and an uncertainty of 10 % (Xu et al., 2013). Ozone and CO were measured continuously using Thermo-Fisher Scientific TEI 49i and TEI 48i, respectively. The fine particle mass concentration (PM_2.5) was continuously measured with a combined technique of light scattering photometry and beta radiation attenuation (Thermo Scientific SHARP Monitor Model 5030). Water-soluble aerosol ions (${\mathrm{NO}}_{\mathrm{3}}^{-}$, ${\mathrm{SO}}_{\mathrm{4}}^{\mathrm{2}-}$, ${\mathrm{NH}}_{\mathrm{4}}^{+}$, etc.) and ammonia (NH₃) were measured by a Monitor for Aerosols and Gases in ambient Air (designed and manufactured by Applikon Analytical B.V., the Netherlands) with a PM_2.5 cyclone inlet, at a time resolution of 1 h. The size distribution of submicron particles (6–820 nm) is measured with a DMPS (differential mobility particle sizer) constructed at the University of Helsinki in Finland. Meteorological measurements including relative humidity (RH), wind speed, wind direction, and air temperature were recorded by Automatic Weather Station (CAMPEEL co., AG1000). UVB total radiation was measured by a UVB radiometer (UVS-B-T UV Radiometer, KIPP & ZONEN).

2.2 TUV model and OH estimate

The Tropospheric Ultraviolet and Visible (TUV) radiation model (https://www2.acom.ucar.edu/modeling/tropospheric-ultraviolet-and-visible-tuv-radiation-model, last access: 10 October 2019) was adopted to compute the photolysis frequencies, which is most probably accurate in clean and cloudless days. The pivotal parameters of this model were inputted as follows: the ozone density was measured by the Ozone Monitoring Instrument (OMI); the typical single scattering albedo (SSA) and Ångström exponent (Alpha) were 0.93 and 1.04 (Shen et al., 2018). The mean value of optical depth (AOD) at 550 nm was 0.64, derived following an empirical relationship with PM_2.5 in Nanjing (Shao et al., 2017). To reduce the error of the model, we used observed UVB to correct simulated results (J_mod) by Eq. (1).

$$\begin{array}{}\text{(1)}& J={\displaystyle \frac{{\mathrm{UVB}}_{\mathrm{obs}}}{{\mathrm{UVB}}_{\mathrm{mod}}}}{J}_{\mathrm{mod}}\end{array}$$

The daytime OH concentration was calculated by applying the empirical model (Eq. 2) proposed by Rohrer and Berresheim (2006), based on strong nearly linear correlations of measured OH concentrations with simultaneously observed J(O¹D). The coefficient a reflects the average influence of reactants (e.g., NO_x, VOCs, ozone, H₂O) on OH at the selected place for research; the exponent b represents the combined effects of all photolytic processes on OH, for example, J(O¹D), J(NO₂), J(HONO), and J(HCHO); and the parameter c counts the light-independent OH sources. The values of coefficients a, b and c in Eq. (2) are adopted from the OH studies in the Pearl River delta (PRD) and Beijing, China (Rohrer et al., 2014; Tan et al., 2017, 2018). By summarizing the coefficients a, b, and c in different OH observation campaigns (Table S1 in the Supplement), especially the almost equal slope of the OH–J(O¹D) relation for different locations and seasons in the polluted areas of China, we can make assumptions that the comprehensive impact of reactants (e.g., NO_x and VOCs) on OH cannot compete with that of UV light to OH, and the chemical environments of OH are similar. This suggests that it can be a reasonable way to derive OH by using Eq. (2) in our study, and the error of derived OH radicals has been assessed as not subverting the relative conclusions in this study (Fig. S1a and d). The calculated OH concentrations around noon (J(O¹D)) > $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹) were in the range of 0.46–2.0×10⁷ cm⁻³, comparable to observations in Chinese urban or suburban atmospheres (Lu et al., 2012, 2013).

$$\begin{array}{}\text{(2)}& \begin{array}{rl}& \left[\mathrm{OH}\right]=a\times \left(\mathrm{J}({\mathrm{O}}^{\mathrm{1}}\mathrm{D}\right)/{\mathrm{10}}^{-\mathrm{5}}{\mathrm{s}}^{-\mathrm{1}}{)}^b+c\\ & a=\mathrm{4.2}\times {\mathrm{10}}^{\mathrm{6}}{\mathrm{cm}}^{-\mathrm{3}},b=\mathrm{1}\\ & c=\mathrm{1.0}\times {\mathrm{10}}^{\mathrm{6}}{\mathrm{cm}}^{-\mathrm{3}}\text{in summer}\\ & c=\mathrm{0.6}\times {\mathrm{10}}^{\mathrm{6}}{\mathrm{cm}}^{-\mathrm{3}}\text{in spring, autumn}\\ & c=\mathrm{0.2}\times {\mathrm{10}}^{\mathrm{6}}{\mathrm{cm}}^{-\mathrm{3}}\text{in winter}\end{array}\end{array}$$

Figure 1 Monthly variations of (a) HONO, (b) HONO∕NO_x, (c) NO_x, (d) PM_2.5, (e) RH and (f) T. The solid bold lines are median values, the markers indicate mean values, and the shaded areas represent percentiles of 75 % and 25 %. In (a) and (b), values in February are linearly interpolated based on the data from the months before and after, since there were only a few days when HONO was observed in February. In (c), the shaded area is colored by the 25th to 75th percentiles of NO.

3 Results

3.1 Observation overview

We carried out continuous measurements for HONO at the SORPES station in the northeastern suburb of Nanjing from November 2017 to November 2018 with a mean measured ambient HONO mixing level of 0.69±0.58 ppb (Fig. S2), within the range of those in the center or vicinity of megacities (Table 2). Figure 1 shows the seasonal pattern of HONO and related parameters. The highest concentration of HONO is found in winter (1.04±0.75 ppb), followed by spring (0.68±0.48 ppb), autumn (0.66±0.53 ppb) and summer (0.45±0.37 ppb). Such seasonal variations in Nanjing are aligned with that in Beijing (Hendrick et al., 2014) and are somewhat similar to those in Jinan (Li et al., 2018), where the highest levels occurred in winter and the lowest levels occurred in autumn, but these variations are different from those in Hongkong (Xu et al., 2015), where the highest and lowest values of HONO appeared in autumn and spring, respectively. The important point is that the seasonality of HONO coincides with that of NO_x (or NO₂), which is believed to be the main precursor of HONO in current studies.

Table 2 Overview of the measured HONO and NO_x levels in Nanjing and comparison with other urban or suburban sites.

(1) Acker et al. (2006); (2) Yu et al. (2009); (3) Kanaya et al. (2007); (4) Elshorbany et al. (2009); (5) Dusanter et al. (2009); (6) Wong et al. (2011); (7) Bernard et al. (2016); (8) Xu et al. (2015); (9) Tong et al. (2015); (10) Huang et al. (2017); (11) Li et al. (2018).

The HONO-to-NO_x ratio or the HONO-to-NO₂ ratio has been used extensively in previous studies to characterize the HONO levels and to indicate the extent of heterogeneous conversion of NO₂ to HONO, since it is less influenced by convection or transport processes than the individual concentration (Lammel and Cape, 1996; Stutz et al., 2002). When a large proportion of HONO comes from direct emissions, the value of HONO∕NO₂ usually becomes larger, falsely implying the strong formation of HONO from NO₂. However, the freshly emitted air masses generally have the lowest HONO∕NO_x ratio, meaning that HONO∕NO_x behaves better than HONO∕NO₂ in a way. As shown in Fig. 1b, the low value of HONO∕NO_x in winter is attributed to heavy emissions because we see high mixing ratios of NO during this cold season (Fig. 1c); the reasons for the two peaks of HONO∕NO_x in spring and summer will be discussed in Sects. 3.3, 3.4 and 4.

Figure 2 Diurnal variations of HONO, NO, NO₂, HONO∕NO_x, and UVB in (a) winter, (b) spring, (c) summer, and (d) autumn. The levels of NO, NO₂ and UVB are displayed as their mean concentrations.

All daily changes in HONO concentration in different seasons closely resemble a cycle where HONO peaks in the early morning and then decreases to the minimum in the late afternoon, following the diurnal trend of NO_x (Fig. 2). The daily variations of HONO in Nanjing are like those seen in other urban areas (Villena et al., 2011a; Wang et al., 2013; Michoud et al., 2014; Lee et al., 2016), but differ from observations on the roadside (Rappenglück et al., 2013; Xu et al., 2015). At night, the mixing ratio of HONO increases rapidly in the first few hours and then stabilizes (in spring and summer) or gradually climbs to its peak in the morning rush hour (in winter and autumn). The accumulation during nighttime hours suggests a significant production of HONO exceeding the dry deposition of HONO. As the sun rises, the HONO sink will be strengthened by the photolysis and vertical mixing processes, resulting in the peak times of the diurnal patterns of HONO concentration varying in different seasons. During the daytime, the rate of HONO abatement is rapid before noon and then becomes progressive until HONO concentration falls to the minimum. Given that the photolytic lifetime of HONO is about 10–20 min at midday (Stutz et al., 2000), the considerable HONO concentration during daytime indicates the existence of strong production of HONO.

From the daily variations of the HONO-to-NO_x ratio, we can further understand the behavior of HONO in the atmosphere. The HONO∕NO_x ratio is regularly enhanced quickly before midnight then reaches a maximum during the latter half of the night. According to Stutz et al. (2002), the highest HONO∕NO_x (or HONO∕NO₂) is defined by the balance between production and loss of HONO each night; the conditions affecting the highest achievable ratio at nighttime will be discussed in Sect. 3.3. What is interesting here is the peak of the HONO∕NO_x ratio in the midday sun in spring, summer and autumn, and even in winter, the ratio does not decline, but remains stationary before and at noon. If the HONO sources during the daytime are consistent with those at night, the minimum HONO∕NO_x ratio should occur at noon due to the intense photochemical loss of HONO. Therefore, there must be additional sources of HONO during daytime (e.g., Reaction R3). The increase in HONO∕NO_x with solar radiation (e.g., UVB) is found in both diurnal and seasonal variations, indicating that these daytime sources have a relationship with the intensity of solar radiation. We will further discuss the potential daytime sources of HONO in Sect. 3.4.

The elevated mixing ratio of HONO presents an efficient source of OH radicals during daytime in Nanjing. We calculate the OH production rate from HONO, i.e., P_OH(HONO), using Eq. (3). As discussed in Su et al. (2008b) and Li et al. (2014), HONO produced by the reaction of NO with OH (Reaction R3) is actually a temporary reservoir of OH radicals. The photolysis of HONO from this pathway only regenerates OH radicals and cannot contribute to the concentrations of OH radicals. So it is inappropriate to estimate the primary OH production from HONO based on P_OH(HONO) derived from Eq. (3). For comparison, the OH production rate from ozone photolysis, P_OH(O₃), is derived from Eq. (4). Only part of the O(¹D) atoms, formed by the photolysis of O₃ at wavelengths below 320 nm (Reaction R7), can produce OH radicals by reacting with water (Reaction R8) in the atmosphere, so we use the absolute water concentration, which can be derived from relative humidity and temperature, to calculate the branching ratio of O(¹D)(ϕ_OH) between Reactions (R8) and (R9). The reaction rate of O(¹D) with O₂ is $\mathrm{4.0}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molecules⁻¹ s⁻¹ and the reaction rate of O(¹D) with N₂ is $\mathrm{3.1}\times {\mathrm{10}}^{-\mathrm{11}}$ cm³ molecules⁻¹ s⁻¹ (Seinfeld and Pandis, 2016). In addition to the two mechanisms mentioned above, there are other pathways to generate primary OH radicals: the photolysis of aldehydes, mainly HCHO, can form HO₂ radicals and then convert to OH radicals by reacting with NO; the reactions of ozone with alkenes produce OH radicals directly (Finlayson-Pitts and Pitts, 2000; Seinfeld and Pandis, 2016).

$$\begin{array}{}\text{(3)}& {\displaystyle }{P}_{\mathrm{OH}}\left(\mathrm{HONO}\right)=\mathrm{J}\left(\mathrm{HONO}\right)\left[\mathrm{HONO}\right]\text{(4)}& {\displaystyle }\begin{array}{rl}& P_{\mathrm{OH}}\left({\mathrm{O}}_{\mathrm{3}}\right)=\mathrm{2}\mathrm{J}\left({\mathrm{O}}^{\mathrm{1}}\mathrm{D}\right)\left[{\mathrm{O}}_{\mathrm{3}}\right]{\mathit{\varphi }}_{\mathrm{OH}}\\ & {\mathit{\varphi }}_{\mathrm{OH}}=k_{\mathrm{8}}\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]/\left(k_{\mathrm{8}}\right[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}]+k_{\mathrm{9}}[\mathrm{M}\left]\right)\end{array}\end{array}$$

$$\begin{array}{}\text{(R7)}& {\displaystyle }{\mathrm{O}}_{\mathrm{3}}+h\mathit{\upsilon }\to \mathrm{O}{(}^{\mathrm{1}}\mathrm{D})+{\mathrm{O}}_{\mathrm{2}}(\mathit{\lambda }<\mathrm{320}\mathrm{nm})\text{(R8)}& {\displaystyle }\mathrm{O}{(}^{\mathrm{1}}\mathrm{D})+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\to \mathrm{2}\mathrm{OH}\text{(R9)}& {\displaystyle }\mathrm{O}{(}^{\mathrm{1}}\mathrm{D})+\mathrm{M}\to \mathrm{O}{(}^{\mathrm{3}}\mathrm{P})+\mathrm{M}\left(\mathrm{M}\mathrm{is}{\mathrm{N}}_{\mathrm{2}}\mathrm{or}{\mathrm{O}}_{\mathrm{2}}\right)\end{array}$$

Figure 3 shows that the diurnal peak of OH production rate from HONO is usually found in the late morning, caused by the combined effects of HONO concentration and its photolysis frequency, and the seasonal peak of P_OH(HONO) occurs in spring for the same reason. P_OH(O₃), coinciding with the trend of J(O¹D), is highest around noon at a daily timescale and is highest in summer at a seasonal timescale, respectively. Significantly, the photolysis of HONO produces more OH than that of ozone throughout the daytime in winter, spring, and autumn. In summer, the contribution of HONO to OH is greater in the early morning, and although the photolysis of ozone contributes more OH at noon, the role of HONO is considerable. Overall, the average P_OH(HONO) during 08:00–16:00 LT is 1.16 ppb h⁻¹ and the mean value of P_OH(O₃) is 0.41 ppb h⁻¹. The impressive role of HONO in the atmospheric oxidizing capacity should benefit photochemical ozone production (Ding et al., 2013; Xu et al., 2017, 2018), new particle formation (Qi et al., 2015) and secondary aerosol formation (Xie et al., 2015; Sun et al., 2018) in Nanjing, western YRD region.

Figure 3 Averaged OH production rates from photolysis of HONO and ozone in (a) winter, (b) spring, (c) summer, and (d) autumn.

3.2 Direct emissions of HONO from combustion

As mentioned above, the good correlation of HONO with NO_x (Fig. 4a) and the similar patterns of HONO and NO_x, particularly sharply increasing together in the fresh plumes, in which the NO∕NO_x ratios are usually very high (Fig. S2), indicate the presence of direct combustion emission of HONO, which need to be deducted when analyzing the secondary formation of HONO. The SORPES station is influenced by air masses from both industries and vehicles (Ding et al., 2016), so the traffic emission factor investigated in other experiments cannot be used directly. We derive the emitted HONO∕NO_x ratio according to the method of Xu et al. (2015), and the following criteria are adopted to select fresh plumes: (a) [NO_x] > 40 ppbv; (b) NO∕NO_x > 0.85; (c) good correlation between HONO and NO_x(r > 0.9); (d) short duration of plumes (< =2 h); and (e) [UVB] < =0.01 W m⁻². Then, the slopes of HONO to NO_x in selected plumes were considered the emission ratios in our study.

Figure 4 (a) The relationship between HONO and NO_x colored by the NO∕NO_x ratio. The dotted line is the emission ratio derived in this study and the solid line is obtained from simple linear fitting; (b) average emission contribution ratios for different concentrations of HONO and the frequency distribution of HONO concentrations. Both (a) and (b) are nighttime values.

Within the 1-year dataset, we select 55 freshly emitted plumes satisfying the criteria above (Table S2), of which 20 air masses were found in the morning and evening rush hours; the derived HONO∕NO_x ratios vary from 0.26 % to 1.91 %, with a mean value of 0.79 %±0.36 %. Many factors, such as the amount of excess oxygen, the types of fuel used (gasoline, diesel, coal), whether engines are catalyst-equipped, and whether engines are well-maintained, could result in variances in these ratios. Additionally, the rapid heterogeneous reduction of NO₂ on synchronously emitted BC can also raise the value of HONO∕NO_x (Xu et al., 2015). For our study, an average emission factor of 0.79 % is deployed to evaluate the emission contribution of HONO (Eq. 5), which is abbreviated as HONO_emis.

$$\begin{array}{}\text{(5)}& {\displaystyle }{\mathrm{HONO}}_{\mathrm{emis}}={\mathrm{NO}}_x\times \mathrm{0.0079}\text{(6)}& {\displaystyle }{\mathrm{HONO}}_{\mathrm{corr}}=\mathrm{HONO}-{\mathrm{HONO}}_{\mathrm{emis}}\end{array}$$

Combustion emissions contribute an average of 23 % of total measured HONO concentrations at night (Fig. 4b), with a maximum HONO_emis∕HONO value of 32 % in winter and a minimum HONO_emis∕HONO value of 18 % in summer. We then get the corrected observed HONO (HONO_corr) by Eq. (6) for further analysis. The slope of the fitted line for HONO and NO_x is 1.62 %, higher than the emission ratio of 0.79 % (Fig. 4a), and almost 80 % of HONO is from HONO_corr that is not affected by emissions (Fig. 4b). These imply significant secondary formation of HONO in the atmosphere.

3.3 Heterogeneous conversion of NO₂ to HONO at nighttime

3.3.1 The NO₂-to-HONO conversion rate (C_HONO)

In addition to emissions, heterogeneous reactions of NO₂ on surfaces (Reactions R4 and R5) are believed to be the major formation pathways of nocturnal HONO. Thus, the NO₂-to-HONO conversion rate is calculated from Eq. (5) (Alicke et al., 2002; Alicke, 2003; Wentzell et al., 2010), where NO₂ is adopted to scale HONO to reduce the dilution influence according to Su et al. (2008a). Similarly to HONO∕NO_x (Fig. 2), the nighttime HONO_corr∕NO₂ ratio rises from the lowest value and then reaches a quasi-stable state, meaning that C_HONO can actually be used to assess how quickly HONO_corr∕NO₂ can increase to its equilibrium.

$$\begin{array}{}\text{(7)}& C_{\mathrm{HONO}}={\displaystyle \frac{\frac{[{\mathrm{HONO}}_{\mathrm{corr}}{]}_{\left(t_{\mathrm{2}}\right)}}{[{\mathrm{NO}}_{\mathrm{2}}{]}_{\left(t_{\mathrm{2}}\right)}}-\frac{[{\mathrm{HONO}}_{\mathrm{corr}}{]}_{\left(t_{\mathrm{1}}\right)}}{[{\mathrm{NO}}_{\mathrm{2}}{]}_{\left(t_{\mathrm{1}}\right)}}}{t_{\mathrm{2}}-t_{\mathrm{1}}}}\end{array}$$

Following the method of Xu et al. (2015) and Li et al. (2018), 137 cases in which HONO_corr∕NO₂ increased almost linearly from 18:00 to 24:00 each night are selected, and the slope fitted by the least linear regression for HONO_corr∕NO₂ against time is just the conversion frequency of NO₂ to HONO. The derived C_HONO varies from 0.0043±0.0017 h⁻¹ in winter to 0.0066±0.0040 h⁻¹ in summer, with an average value of 0.0055±0.0032 h⁻¹, which is in the range (0.004–0.014 h⁻¹) shown by other studies in urban and suburban sites (Fig. 5). Note that C_HONO assumes all the increase in HONO_corr∕NO₂ is caused by the conversion of NO₂, excluding other possible sources of HONO (e.g., soil nitrite); and the computed C_HONO is the net NO₂-to-HONO conversion rate since the measured HONO_corr has already taken the sinks of HONO (mainly deposition) into account. Considering the uncertainties of C_HONO, utilizing C_HONO directly to analyze the mechanism of HONO formation thoroughly may not be appropriate, but it could be attemptable to facilitate the parameterizations for HONO production in air quality models by C_HONO when the chemical mechanisms are not clear yet.

Figure 5 Comparison of observed NO₂-to-HONO conversion rates in cities: Nanjing (this study); Mainz (Lammel, 1999); Hongkong (Xu et al., 2015); Jinan (Li et al., 2018); Shanghai (Wang et al., 2013); Beijing (Wang et al., 2017); Milan (Alicke et al., 2002); and Kathmandu (Yu et al., 2009).

3.3.2 RH dependence of HONO chemistry

It appears that NO₂ hydrolysis on humid surfaces (Reaction R4), having a first-order dependence on NO₂ (Jenkin et al., 1988; Ackermann, 2000; Finlayson-Pitts et al., 2003), is influenced by the surface-absorbed water (Kleffmann et al., 1998; Finlayson-Pitts et al., 2003), although the exact mechanisms are still unknown. In the studies of Stutz et al. (2002) and Stutz et al. (2004), the pseudo steady state of HONO∕NO₂, where this ratio is at a maximum at nighttime, is presumed to be a balance between the production of HONO from NO₂ and the loss of HONO on surfaces, and the highest HONO∕NO₂ value is determined by the ratio of the reactive uptake coefficients for each process. Scatter plots of HONO_corr∕NO₂ against relative humidity in our study are illustrated in Fig. 6. To eliminate as much influence of other factors as possible, the average of the six highest HONO_corr∕NO₂ values in each 5 % RH interval is calculated according to Stutz et al. (2004). The phenomenon that HONO_corr∕NO₂ first increases and then decreases with an increasing RH in Fig. 6a was also observed by other studies (Hao et al., 2006; Yu et al., 2009; Li et al., 2012; Wang et al., 2013). The dependencies of HONO_corr∕NO₂ on RH and the possible reasons or mechanisms are discussed as follows. Even at the lowest measured RH of 18 %, the absolute moisture content in the atmosphere is still greater than 10³ ppm in our study, which is quite abundant for reacting with NO₂, but the HONO_corr∕NO₂ ratio is quite small and remains unchanged when RH is below 45 %, indicating that the NO₂ to HONO conversion efficiency should be determined by water covering the surfaces rather than by the amount of water in the air.

Figure 6 Scatter plots of the HONO_corr∕NO₂ ratio and RH during nighttime, separating the data into (a) clean hours (hourly mean PM_2.5 < 25 µg m⁻³) and (b) polluted hours (hourly mean PM_2.5 > 75 µg m⁻³). Triangles are the averaged top-six HONO_corr∕NO₂ in each 5 % RH interval, and the error bars are the standard deviations. The overall average concentrations of PM_2.5 in (a) and (b) are shown to the right of the figures.

It has been reported that surfaced absorbed water depends on RH values, and the dependences vary for different material surfaces of the ground, but generally follow the shape of a BET isotherm (Lammel, 1999; Saliba et al., 2001; Sumner et al., 2004). The number of mono-layers of water increases slowly from zero to 2–4, accompanied by RH from zero to a turning point, and the water coverage grows dramatically (up to 10–100 mono-layers) once RH exceeds the turning point (Finlayson-Pitts et al., 2003). Figure 6a shows the case where the surface for NO₂ converting to HONO is dominated by the ground and the HONO_corr∕NO₂ increases along with RH when RH is less than 75 %, which can be explained by the reaction of NO₂ to generate HONO on wet surfaces. However, a negative correlation between HONO_corr∕NO₂ and RH is found when RH is over 75 %, presumably because the rapidly growing aqueous layers of the ground surface lead to efficient uptake of HONO and make the surface less accessible or less reactive to NO₂. Hence, the RH turning point for absorbed water on ground surfaces is perhaps around 75 % for our observation, within the range of results from experiments on various surfaces (RH: 70 %–80 %) (Lammel, 1999; Saliba et al., 2001; Sumner et al., 2004). Once RH exceeds 95 %, the reaction surface asymptotically approaches the state of a water droplet, where the quite limited formation of HONO and the extremely impactful loss of HONO will result in a dramatic decline of the HONO_corr∕NO₂ ratio (Fig. 6a and b).

Notably, the constant HONO_corr∕NO₂ value at RH between 75 % and 95 % under the condition of high PM_2.5 mass loading (Fig. 6b), compared to the downward trend of HONO_corr∕NO₂ within the same humidity range in low PM_2.5 mass concentration (Fig. 6a), implies a contribution of aerosol surfaces to the NO₂–HONO conversion. Since both HONO_corr∕NO₂ in Fig. 6a and b are affected by the ground surfaces, we can use the difference of HONO_corr∕NO₂ between the two figures to represent the influence of aerosol. As the area of shadow showed in Fig. 6b, the aerosol-affected HONO_corr∕NO₂ is positively related to RH before RH reaches 95 %. With the increase in RH, the hygroscopic growth of aerosol particles should provide a larger surface area. When RH is higher than 75 %, which has exceeded the mutual deliquescence relative humidity of inorganic salts (Fountoukis and Nenes, 2007), aerosols will transfer to aqueous phase gradually and then promote multiphase or heterogeneous chemistry processes (Herrmann et al., 2015). For example, the oxidation of SO₂ by NO₂ on an aqueous aerosol surface may produce ${\mathrm{NO}}_{\mathrm{2}}^{-}/\mathrm{HONO}$ efficiently under polluted conditions (Xie et al., 2015; Wang et al., 2016). In addition, the enhancement NO₂ uptake on micro-droplets by anions has been reported in experiments (Yabushita et al., 2009).

Figure 7 (a) The correlation between HONO_corr and PM_2.5 and (b) the correlation between HONO_corr∕NO₂ and PM_2.5; all scatters come from the time (03:00–06:00 LT) when the HONO_corr∕NO₂ ratio reaches the pseudo steady state each night and are colored by NH₃∕CO. In (b), the larger triangles with gray borders depict the measured data from November to May, and the boxplot in each 30 µg m⁻³ interval of PM_2.5 is illustrated according to the same data, the red box boundaries represent interquartile range, the whiskers represent the 10 %–90 % percentile range, the horizontal red lines represent median values, and the red markers represent mean values. The correlation coefficient and the slope of the linearly fitted line in (b) are derived from the averaged HONO_corr∕NO₂ and averaged PM_2.5 in each box.

3.3.3 Impact of aerosols on HONO formation

To further understand the heterogeneous formation of HONO on aerosol, we carry out a correlation analysis when HONO_corr∕NO₂ reaches the pseudo steady state at each night (03:00–06:00 LT). The convergence or diffusion processes of gases and particles can also lead to a consistent trend of HONO_corr and PM_2.5 (Fig. 7a), while the ratio of HONO_corr and NO₂ can not only reduce this physical effect, but can also represent the conversion degree of NO₂ to HONO, so a moderate positive correlation between HONO_corr∕NO₂ and PM_2.5 ($r=\mathrm{0.35},p=\mathrm{0.01}$) throughout the observation period could be more believable (Fig. 7b). As shown by larger triangles with gray borders in Fig. 7b, HONO_corr∕NO₂ is better correlated with PM_2.5 in the months when the mass concentrations of PM_2.5 are higher during this 1-year measurement, generally occurring from November to May (Fig. 1d). This finding can be explained with a law that greater contributions of NO₂ heterogeneously reacting on aerosol surface to HONO cause better correlations between HONO_corr∕NO₂ and PM_2.5. Interestingly, this relationship can also be divided approximately into two groups by NH₃∕CO; the correlation is good when the value of NH₃∕CO is lower than 2 ‰, but when NH₃∕CO is higher than 2 ‰, a poor correlation is found. We will discuss this phenomenon further in Sect. 4. The evidence of HONO formation on aerosol was also found in other observations (Reisinger, 2000; Wang, 2003; Li et al., 2012; Nie et al., 2015; Hou et al., 2016; Cui et al., 2018).

As is known, producing HONO is not the dominant sink of NO₂ at night, but it seems that more NO₂ can be converted to HONO under conditions of heavy pollution (Fig. 7b). We discuss whether heterogeneous reactions of NO₂ on aerosols are able to provide comparable HONO with our measurement by Eq. (8), only considering HONO formation on particle surfaces and assuming that HONO principally settles on the ground surface, neglecting HONO loss on aerosol. $c_{{\mathrm{NO}}_{\mathrm{2}}}$ is the mean molecular velocity of NO₂ (370 m s⁻¹); ${\left[\frac{S}{V}\right]}_{\mathrm{aer}}$ is the surface area to volume ratio (m⁻¹) of aerosol; ν_HONO is the deposition velocity of HONO, which is considered to be close to the deposition velocity of NO₂ at night (Stutz et al., 2002; Su et al., 2008a); and an approximate value of 0.1 cm s⁻¹ is used based on the measurements from Coe and Gallagher (1992) and Stutz et al. (2002); H is the boundary layer mixing depth, and a value of 100 m is assumed for nighttime (Su et al., 2008a).

$$\begin{array}{}\text{(8)}& C_{\mathrm{HONO}}={\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}{\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}{c}_{{\mathrm{NO}}_{\mathrm{2}}}{\left[{\displaystyle \frac{S}{V}}\right]}_{\mathrm{aer}}-{\displaystyle \frac{{\mathit{\nu }}_{\mathrm{HONO}}}{H}}{\displaystyle \frac{\left[\mathrm{HONO}\right]}{\left[{\mathrm{NO}}_{\mathrm{2}}\right]}}\end{array}$$

Considering the nighttime period with severe haze, the aerosol surface density calculated from the particle number size distributions between 6 and 800 nm is about $\mathrm{1.2}\times {\mathrm{10}}^{-\mathrm{3}}$ m⁻¹, matched by 200 µg m⁻³ of PM_2.5 from our observations, and the averaged mixing ratios of HONO and NO₂ are 1.15 and 28.4 ppb, respectively (Table 2). For 30 %–100 % of the measured mean C_HONO (0.0043 h⁻¹) in winter, the uptake coefficient of NO₂ to HONO (${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$) calculated from Eq. (8) is in the range of $\mathrm{6.9}\times {\mathrm{10}}^{-\mathrm{6}}$ to $\mathrm{1.44}\times {\mathrm{10}}^{-\mathrm{5}}$, consistent with the results from many laboratory studies which demonstrate that the uptake coefficients of NO₂ (${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}}$) on multiple aerosol surfaces or wet surfaces are mainly distributed around 10⁻⁵, with the HONO yield varying from 0.1 to 0.9 (Grassian, 2002; Aubin and Abbatt, 2007; Khalizov et al., 2010; Han et al., 2017). It is necessary to elaborate that (1) the ambient particles were dried with silica gel before measuring their number size distributions, and the mass concentrations of PM_2.5 were also measured under a system where the temperature was maintained at 30^∘, usually above ambient temperature; (2) the aerosol surface was calculated by assuming that all particles are spherically shaped, but the particles could in fact have irregular bodies and a porous structure; (3) the particle size of both PM_2.5 and derived $[\frac{S}{V}{]}_{\mathrm{aer}}$ is just a part of the total suspended particulate matter. As described, the aerosol surface in the atmosphere is actually underestimated in our study, and thus the ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ we derived could be the upper limit of the uptake coefficient for NO₂ conversion to HONO on aerosol. In addition to particle surfaces, other aerosol parameters such as surface water content, chemical composition, pH value, and phase state of surfaces may also influence the heterogeneous formation of HONO.

3.4 Missing daytime HONO source

After discussing the nocturnal formation mechanism of HONO, we now focus on the chemistry of daytime HONO whose concentrations are still about 0.25–0.6 ppb at noon with a lifetime of only 10–20 min (Fig. 2). We are not certain whether the observed HONO can be provided by known mechanisms (gas-phase Reaction R4 and emissions) to date, so a budget equation of daytime HONO (Eq. 9) is utilized to analyze its sources and sinks (Su et al., 2008b; Sörgel et al., 2011). Here, dHONO ∕ dt is the change rate of the observed HONO. The source rates of HONO contain the homogeneous formation rate (P_NO+OH, Reaction R3); the combustion emission rate (P_emis); and the unknown HONO daytime source (P_unknown). The sink rates of HONO consist of the photolysis rate (L_phot, Reaction R1); the reaction rate of HONO with OH (L_HONO+OH, Reaction R2); and the dry deposition rate (L_dep). T_v and T_h represent the vertical (T_v) and horizontal (T_h) transport processes of HONO, which are thought to be negligible for intense radiation and relatively homogeneous atmospheres with generally calm winds (Dillon et al., 2002; Su et al., 2008b; Sörgel et al., 2011).

$$\begin{array}{}\text{(9)}& \begin{array}{rl}{\displaystyle \frac{\mathrm{dHONO}}{\mathrm{d}t}}& =(P_{\mathrm{NO}+\mathrm{OH}}+P_{\mathrm{emis}}+P_{\mathrm{unknown}})\\ & -(L_{\mathrm{phot}}+L_{\mathrm{HONO}+\mathrm{OH}}+L_{\mathrm{dep}})+T_{\mathrm{v}}+T_{\mathrm{h}}\end{array}\end{array}$$

Therefore, the undiscovered daytime source of HONO (P_unknown) can be derived by Eq. (10), which is a deformation of Eq. (9) without minor terms (T_v and T_h) and where dHONO ∕ dt is substituted by ΔHONO ∕ Δt that is counted as the difference between observed HONO at two time points. The reaction rate constants of Reaction (R2) (k_HONO+OH) and Reaction (R3) (k_NO+OH) are $\mathrm{6.0}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ molecules⁻¹ s⁻¹ and $\mathrm{9.8}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ molecules⁻¹ s⁻¹, respectively (Atkinson et al., 2004). The emission ratio of HONO to NO_x(HONO∕NO_x= 0.79 %) obtained in Sect. 3.2 is used to estimate P_emis. For L_dep, the dry deposition velocity of diurnal HONO (ν_HONO) is measured as 2 cm s⁻¹ in the work of Harrison et al. (1996), and a practical mixing height of 200 m is adopted, considering that most of the HONO cannot rise above this altitude due to rapid photolysis (Alicke et al., 2002). Although we did not observe OH radicals directly, the uncertainty of P_unknown caused by the calculated OH radicals from Eq. (2) can be reduced substantially in the case of a low concentration of NO and a high value of J(O¹D) (Fig. S1d).

$$\begin{array}{}\text{(10)}& \begin{array}{rl}{P}_{\mathrm{unknown}}& =\mathrm{J}\left(\mathrm{HONO}\right)\left[\mathrm{HONO}\right]\\ & +k_{\mathrm{HONO}+\mathrm{OH}}\left[\mathrm{HONO}\right]\left[\mathrm{OH}\right]\\ & +{\displaystyle \frac{{\mathit{\nu }}_{{}_{\mathrm{HONO}}}}{H}}\left[\mathrm{HONO}\right]+{\displaystyle \frac{\mathrm{\Delta }\mathrm{HONO}}{\mathrm{\Delta }t}}\\ & -k_{\mathrm{NO}+\mathrm{OH}}\left[\mathrm{NO}\right]\left[\mathrm{OH}\right]-{\displaystyle \frac{\mathrm{0.79}\mathit{\%}\times \mathrm{\Delta }{\mathrm{NO}}_x}{\mathrm{\Delta }t}}\end{array}\end{array}$$

Figure 8 shows the average daytime HONO budgets from 08:00 to 16:00 LT during different seasons. The major loss route of HONO is photodecomposition (L_phot) with an average value of 1.50 ppb h⁻¹ around noontime (10:00–14:00 LT); the next is dry deposition (L_dep), whose mean value at the same time is 0.21 ppb h⁻¹, and by L_HONO+OH, which is less than 5 % of that of L_phot. For the sources of HONO around noon, the average homogeneous reaction rate between NO and OH (P_NO+OH) is 0.63 ppb h⁻¹, and P_emis just gives a tiny part of HONO at a rate of 0.02 ppb h⁻¹, meaning that most HONO comes from an unknown source whose average rate (P_unknown) is 1.04 ppb h⁻¹, contributing about 61 % of the production of HONO. Comparing summer data, the mean unknown daytime source strength of HONO in Nanjing is almost at the upper–middle level of those reported in the existing literature: 0.22 ppb h⁻¹ at a rural site of New York State, USA (Zhou et al., 2002); 0.5 ppb h⁻¹ in a forest near Jülich, Germany (Kleffmann, 2005); 0.77 ppb h⁻¹ in a polluted rural area of the Pearl River delta, China (Li et al., 2012); 0.98 ppb h⁻¹ at an urban site in Xi'an, China (Huang et al., 2017); 1.7 ppb h⁻¹ in an urban area of Santiago, Chile (Elshorbany et al., 2009); and 2.95 ppb h⁻¹ in the urban atmosphere of Jinan, China (Li et al., 2018). In our study, the OH production rate from the missing HONO accounts for about 53 % of total P_OH(HONO) (Fig. S2), suggesting that the unconventional source of HONO is of significance to atmospheric oxidation.

Figure 8 Averaged daytime HONO budgets and the missing source strength (P_unknown) normalized by NO₂ in (a) winter, (b) spring, (c) summer, and (d) autumn. The mean values of P_unknown around noontime (10:00–14:00 LT) are 0.91 ppb h⁻¹ in winter, 1.61 ppb h⁻¹ in spring, 0.98 ppb h⁻¹ in summer, and 0.68 ppb h⁻¹ in autumn.

Hence, we perform a correlation analysis to explore the potential unknown daytime mechanisms of HONO (Table 3). P_unknown is better correlated with NO₂ × UVB than with NO₂ or UVB alone in winter, spring and autumn (p=0.05), perhaps associated with the photo-enhanced conversion from NO₂ to HONO (George et al., 2005; Stemmler et al., 2006, 2007). The average value of P_unknown normalized by NO₂ is 0.1 h⁻¹, over 18 times greater than the nighttime conversion rate (0.0055 h⁻¹), also implying that P_unknown cannot be explained by the nocturnal mechanism of NO₂ to HONO. Assuming that the height of a well-mixed boundary layer around noon remains constant for each day, UVB × NO₂ and UVB × NO₂ × PM_2.5 could be proxies for photo-induced heterogeneous reactions of NO₂ on ground and aerosol surfaces, respectively. We do not have any solid evidence to identify which surfaces (ground or aerosol) are more important to the photo-heterogeneous reaction of NO₂ based on the present analysis. For the same reason, the photolysis of particulate nitrates (${\mathrm{NO}}_{\mathrm{3}}^{-}$) as a source of HONO (Ye et al., 2016, 2017) cannot be determined as momentous in our study. The comparisons of correlation coefficients shown above follow the method provided by Meng et al. (1992).

Table 3 Correlations of P_unknown against various parameters.

Our study suggests that the missing source of HONO should be considered in the air quality forecasting or regional models to characterize atmospheric oxidizing capacity better, especially in warm seasons (spring and summer). Based on the measurement (Fig. S3), the light-induced heterogeneous conversion of NO₂ to HONO on aerosol surfaces and ground surfaces can probably be included in simulation works, as was done in Lee et al. (2016).

4 Semi-quantitative estimation of the contribution from different sources

From this and previous studies, we can conclude that not only the concentration but also the sources of HONO have temporal and spatial patterns, which is supposed to be considered in model studies. Nocturnal HONO is selected to discuss the monthly variations of HONO sources in detail without the uncertainties of daytime HONO formation, the influences of HONO photolysis, and the mixing effect of the boundary layer. The heterogeneous reaction of NO₂ on aerosol produces a considerable portion of HONO in relatively polluted months (December–May), but contributes very little in clean months (June–October), as seen in Sect. 3.3.3. Coincidentally, direct emissions from burning processes of HONO decrease from their peak values from winter to summer (Sect. 3.2). However, the monthly averaged ratios of HONO to NO_x are highest in summer, which conflicts with the two sources mentioned above.

As is known, a higher NO₂-to-HONO conversion level or other NO_x-independent sources can cause an increase in the HONO∕NO_x ratio. For the case of a mostly constant surface with low reactivity due to the prolonged exposure to oxidizing gases and radiation, the yield of nighttime HONO from NO₂ reacting on ground surfaces could be imprecisely assumed to be unchanged. Thus, soil nitrite formed through microbial activities, especially nitrification by ammonia-oxidizing bacteria (${\mathrm{NH}}_{\mathrm{4}}^{+}\to {\mathrm{NO}}_{\mathrm{2}}^{-}$) (Su et al., 2011; Oswald et al., 2013), is adopted to be a source of atmospheric HONO in this study, considering the nearby presence of some grassland and natural vegetation mosaics. Although we do not directly measure HONO emissions from soil, the observed ammonia can represent its monthly average intensity indirectly, based on the following hypothesis: the dominant source of NH₃ is from soil, especially from fertilizers (${\mathrm{NH}}_{\mathrm{4}}^{+}\to {\mathrm{NH}}_{\mathrm{3}}$), for a good correlation between ammonia and temperature in the site (r=0.63, p=0.01), omitting the contributions of livestock to NH₃ since there is only a small poultry facility within 10 km of this site (Meng et al., 2011; Huang et al., 2012; Behera et al., 2013). Combustion sources (vehicles, industry, biomass burning) should contribute only a fraction of NH₃ seeing that NH₃ is not related to NO_x or CO in our study. Moreover, the releases of both HONO and NH₃ depend on the strength of microbial activities, fertilizing amount, and soil properties (e.g., temperature, acidity and water content of soil). Although the processes of HONO and NH₃ emission from soil may not be completely synchronized, the seasonal patterns for each should be consistent.

Until now, we have been able to separate the sources of HONO into four parts: (1) the combustion emissions from vehicles and industries (HONO_emi) with a constant emitted HONO∕NO_x ratio of 0.79 %; (2) the conversion of NO₂ to HONO on the ground surfaces (HONO_grd) with a constant but unknown yield x₁; (3) the conversion of NO₂ to HONO on aerosol surfaces (HONO_aer) with a PM_2.5-dependent yield (HONO_aer∕NO₂); and (4) the emission from soil (HONO_soi), expressed by corrected NH₃ multiplied by an unknown coefficient x₂. The corrected NH₃ is obtained by subtracting combustion emission from total observed ammonia. Ammonia from combustion is found to be proportional to simultaneous CO (Meng et al., 2011; Chang et al., 2016), and a proportion of 0.3 %, which is in the lower quantile of the NH₃∕CO ratios in fresh air masses (for hourly data: NO∕NO_x > 0.75; UVB=0; temperature < 5 C^∘), is used from our measurements. Substituting monthly average values of measured HONO, NO₂, PM_2.5, NH₃, and CO into Eq. (11) by assuming that HONO_tot is equal to HONO_obs, we can get an overdetermined system of equations which has 11 equations with two unknowns (excluding mean values of related parameters from February), and then we derive an approximate solution (x₁=1.89 %, x₂=1.62 %) by the method of ordinary least squares.

Figure 9 Seasonal variations of four sources of HONO at night (03:00–06:00 LT). The mean normalized error (MNE) of HONO_tot to HONO_obs is 6.42 %.

Figure 9 shows that an average of 36 % of HONO is produced heterogeneously on ground surfaces without perceptible temporal variations, but the contribution of this source is overtaken by NO₂ converting to HONO on aerosols in January (approximately 40 % of HONO) and is exceeded by soil emission in July and August (approximately 40 % of HONO). The seasonal variations of HONO from different pathways at night indicate that short-term observations may just capture a small part of the total picture when exploring the source mechanisms of HONO. The total HONO concentration (HONO_tot) is the sum of derived HONO from the four sources listed above. The good correlation between HONO_tot and HONO_obs and the low mean normalized error of HONO_tot to HONO_obs reveal that our assumption about nocturnal HONO sources is reasonable. It should be noted that the slope of the linearly fitted line between HONO_corr∕NO₂ and PM_2.5 in spring (r=0.74, slope =0.68 ‰) is much higher than that in winter (r=0.60, slope =0.20 ‰), but we just use a mean slope of 0.26 ‰ to evaluate aerosol effects throughout the year: this may be why our method underestimates HONO in March and April and overestimates HONO in January, indicating that the mass concentration of PM_2.5 is not the only factor affecting formation of HONO on aerosols. Besides, lacking considerations of the impact of RH and temperature on NO₂-to-HONO conversion and of seasonal variations in ground surface properties, uncertainties of NO₂-to-HONO conversion mechanisms and of combustion HONO emissions, and lacking direct observation for soil-emitted HONO could all result in the bias between HONO_tot and HONO_obs, so more studies on the detailed mechanism of various HONO sources need to be performed.

$$\begin{array}{}\text{(11)}& \begin{array}{rl}& {\displaystyle \frac{\left[{\mathrm{HONO}}_{\mathrm{grd}}\right]}{\left[{\mathrm{NO}}_{\mathrm{2}}\right]}}=x_{\mathrm{1}}\\ & {\displaystyle \frac{\left[{\mathrm{HONO}}_{\mathrm{aer}}\right]}{\left[{\mathrm{NO}}_{\mathrm{2}}\right]}}=\mathrm{0.26}\mathrm{‰}\times \left[{\mathrm{PM}}_{\mathrm{2.5}}\right]\\ & {\displaystyle \frac{\left[{\mathrm{HONO}}_{\mathrm{emi}}\right]}{\left[{\mathrm{NO}}_x\right]}}=\mathrm{0.79}\mathit{\%}\\ & {\displaystyle \frac{\left[{\mathrm{HONO}}_{\mathrm{soi}}\right]}{\left[{\mathrm{NH}}_{\mathrm{3}}\right]-\mathrm{0.3}\mathit{\%}\times \left[\mathrm{CO}\right]}}=x_{\mathrm{2}}\\ & \left[{\mathrm{HONO}}_{\mathrm{tot}}\right]=\left[{\mathrm{HONO}}_{\mathrm{emi}}\right]+\left[{\mathrm{HONO}}_{\mathrm{soi}}\right]\\ & +\left[{\mathrm{HONO}}_{\mathrm{grd}}\right]+\left[{\mathrm{HONO}}_{\mathrm{aer}}\right]\end{array}\end{array}$$

5 Conclusions

Continuous field measurement of HONO over 1 year was conducted at the SORPES station in Nanjing in the western YRD of China, from December 2017 to December 2018. The observed seasonal average concentrations of HONO are in the range of 0.45–1.04 ppb, which are comparable to those in other urban or suburban regions and appear to be of vital importance to atmospheric oxidation as the OH production rate of HONO is almost 3 times as that of ozone at daytime. HONO and NO_x have coincident monthly variations peaking in December and decreasing to the lowest value in August and have similar diurnal pattern with the highest value in the early morning and a low point in the late afternoon, both indicating that NO_x is a crucial precursor of HONO.

Combustion emissions contribute an average of 23 % to nocturnal HONO concentrations, with an average emission ratio HONO∕NO_x of 0.79 %. During the nighttime, the dominant source of RH-dependent HONO could be the heterogeneous reaction of NO₂ on wet ground or aerosol surfaces with a mean estimated conversion rate of 0.0055 h⁻¹. During the daytime, a missing HONO source with an average strength of 1.04 ppb h⁻¹ was identified around noon, contributing about 61 % of the production of HONO and seeming to be photo-enhanced. HONO released from soil is adopted to discuss the seasonal changes in nocturnal HONO and can contribute 40 % to HONO during summer. Ground formation provides a major part of HONO at a roughly constant proportion of 36 %. The uptake of NO₂ on aerosol surface can generate the greatest amount of HONO during heavily polluted periods (e.g., January). Our results draw a complete picture of the sources of HONO during different seasons and demonstrated the needs of long-term and comprehensive observations to improve the understanding of HONO chemistry.