Urban aerosols and gaseous pollutants were measured in Nanjing in the winter of 2023 (Fig. S1 in the Supplement, Sect. S1). From 17 December 2023 to 10 January 2024, PM2.5 samples were systematically collected for a duration of 23 h daily. The daily averaged concentration of HMS, together with concentrations of other water-soluble inorganic ions within PM2.5, was determined by ion chromatography (Dionex Corp., CA, US). Given that free S(IV) or other S(IV) species, such as aldehyde-S(IV) adducts, may be misidentified as HMS in the IC analysis (Ma et al., 2020; Dingilian et al., 2024), hydrogen peroxide (H2O2) was employed in the analysis process to specifically isolate HMS (Dingilian et al., 2024). The results suggested that the influence of free S(IV) or other S(IV) species on HMS measurement was negligible, as elaborated in Sect. S1 in the Supplement. Carbonaceous components, including organic carbon (OC), elemental carbon (EC), and water-soluble organic carbon (WSOC), were measured using a Sunset OC/EC analyzer (Sunset Laboratory Inc.) and a total organic carbon analyzer (TOC-L, Shimadzu, Kyoto, Japan), respectively. The levels of gaseous pollutants (e.g., SO2, CO, O3) in close proximity to our sampling location were obtained from national urban air quality and real-time publishing platforms (https://quotsoft.net/air/, last access: 15 June 2025). The hourly level of formaldehyde (HCHO) was retrieved from multi-axis differential optical absorption spectroscopy (MAX-DOAS) data (Sect. S2 in the Supplement). To calculate aerosol pH, three semi-volatile gases (NH3, HNO3, and HCl) were also monitored at 30 min intervals using a monitor for aerosols and gases (MARGA; Metrohm Ltd., Switzerland). Meteorological data (RH, temperature, wind speed, visibility, etc.) and backward trajectories (Sect. S3 in the Supplement) were also obtained. In addition, daily PM2.5 samples, gas-phase SO2 samples, and meteorological data were collected onboard during the open research cruise NORC2024-01 conducted in the spring of 2024 (from 13 to 25 April). Compositions of marine aerosols and ambient SO2 levels were also characterized. Details of the sample collection and chemical analysis are described in Sect. S1 in the Supplement.

Recognizing the influence of organic aerosol (OA), especially the WSOC, on aerosol properties, here we integrated two established thermodynamic models, namely the ISORROPIA II and Aerosol Inorganic–Organic Mixtures Functional Groups Activity Coefficient (AIOMFAC) models, to estimate aerosol liquid water content (ALWC), pH, and ionic strength (IS), following the methods delineated in previous work (Battaglia et al., 2019). The ISORROPIA II model (Fountoukis and Nenes, 2007) has gained widespread adoption in estimating aerosol characteristics for atmospheric particles (Nah et al., 2019; Zhang et al., 2024); it considers the thermodynamics of inorganic ions present in aerosol and their equilibrium with gas-phase HNO3, NH3, HCl, and H2O, without consideration of organic constituents. Conversely, the AIOMFAC model (https://aiomfac.lab.mcgill.ca/, last access: 16 September 2024) offers the most extensive consideration of the organic–inorganic interaction but does not solve the equilibrium partitioning calculations. Thus, this study integrated both models to deliver a more comprehensive assessment of aerosol properties. In brief, inorganic PM composition (SO42-, NO3-, Cl-, NH4+, Ca2+, K+, and Mg2+) and gaseous HNO3, NH3, and HCl data observed in urban Nanjing were input into ISORROPIA II under the “Forward” mode and “metastable” state to derive equilibrium concentrations of ALWC and all ionic species present under specified temperature (T) and RH conditions. Subsequently, organic components were incorporated in the inorganic matrix at the same T and RH settings, and the aerosol compositions were simulated using AIOMFAC to calculate the ALWC, pH, and IS. For marine aerosols, we adopted a particle to particle + gas partitioning fraction of NH4+ (ε) of 0.5, drawing from prior observations conducted in the Bohai Sea in May 2021 (Wang et al., 2022a) in light of the absence of gaseous data. Details regarding the model setup and the comparison between model outputs with inorganic-only simulations using ISORROPIA II can be found in Sect. S4 in the Supplement.

In the atmosphere, the formation of HMS requires first that its gas precursors (SO2 and HCHO) dissolve into the water. Dissolved S(IV) (i.e., HSO3- and SO32-) can subsequently react with HCHO(aq), leading to HMS formation: R1HSO3-+HCHO(aq)↔k1HOCH2SO3-,R2SO32-+HCHO(aq)+H2O↔k2HOCH2SO3-+OH-.

These reactions are reversible; the first-order rate constant of HMS decomposition has been measured in previous studies, showing that the decomposition of HMS was so slow that HMS levels are predominantly controlled by formation kinetics in the typical pH range of cloud/fog and aerosol water (pH < 6) (Boyce and Hoffmann, 1984; Deister et al., 1986; Kok et al., 1986; Song et al., 2021). The variables k1 and k2 are the second-order rate constants of Reactions () and (), respectively, where k2 is ≈4 orders of magnitude larger than k1. Thus, the HMS production can be highly sensitive to aerosol acidity, which governs the solubility and distribution of S(IV) species. The rate RHMS (Ms-1) can be represented as 1RHMS=k1×[HSO3-]+k2×[SO32-]×[HCHO(aq)].

Furthermore, the HMS formation rate (PHMS) in ambient aqueous medium (i.e., aerosol water) was calculated in units of µgm-3 h⁻¹: 2PHMS=RHMS×ALWC×3600×MHMS, where ALWC was estimated from thermodynamic models and MHMS is the molar mass of HMS (MHMS = 111 gmol-1). Here we considered the impact of aerosol ionic strength on HMS formation by determining the IS-dependent SO2 solubility and the dissociation of H2SO3, as well as the rate constants (k1 and k2) for Reactions () and (), as detailed in Sect. S5 in the Supplement.

Figure  shows the observations for particulate sulfur-containing species (i.e., HMS and sulfate) and SO2 levels in urban and marine atmospheres, together with PM2.5 compositions, temperature, and relative humidity conditions. In urban Nanjing, a total of 25 daily PM2.5 samples were collected from 17 December 2023 to 10 January 2024. The HMS concentrations ranged from 0.18 to 0.56 µgm-3 (averaging at 0.30 ± 0.10 µgm-3), with corresponding sulfate concentrations varying from 2.06 to 18.03 µgm-3 (7.86 ± 4.54 µgm-3). The HMS/sulfate molar ratios fell between 2.5 % and 8.5 %, averaging at 4.6 ± 1.7 %. During the cruise, 13 marine PM2.5 samples and SO2 samples were synchronously collected from 13 to 25 April 2024. Due to sampler malfunction and limited sampling duration in adverse weather conditions, HMS was only detected in six daily marine aerosol samples, with lower concentrations ranging from 0.03 to 0.07 µgm-3 (0.05 ± 0.01 µgm-3). Despite the restricted sample number, this study provided the first observational evidence on HMS levels in marine atmosphere, roughly aligned with previous model-estimated HMS levels in marine atmosphere (0.03–0.09 µgm-3; Zhao et al., 2024). The ambient concentrations of non-sea-salt sulfate (nss-SO42-) were from 1.50 to 2.70 µgm-3 (2.09 ± 0.46 µgm-3). This notably lower particulate sulfur content in marine aerosols can probably be attributed to the lower gas-phase precursor concentration, evidenced by an average SO2 level of 0.82 ± 0.47 ppb, compared with the SO2 level in urban Nanjing of 2.2 ± 0.7 ppb. In addition, slightly lower HMS / sulfate molar ratios (3.0 ± 1.1 %) were observed in marine atmosphere, considering the biogenic contribution to nss-SO42- in the spring (Zhang et al., 2013).

In addition, a 7 d haze pollution event (from 27 December 2023 to 2 January 2024) was observed in urban Nanjing, where notably elevated levels of HMS and sulfate were observed (P < 0.05). Throughout the haze event (PM2.5 = 114.3 ± 18.0 µgm-3), the average concentrations of HMS and sulfate were 0.36 ± 0.09 and 11.4 ± 4.0 µgm-3, respectively, with a HMS/sulfate molar ratio of 3.5 ± 0.7 % (Table S1 in the Supplement). It is noted that, even on hazy days, the HMS levels in our observations were significantly lower, compared with those reported in northern China during severe winter haze episodes (averaged at 4–7 µgm-3; Ma et al., 2020; Liu et al., 2021a; Chen et al., 2022; Wang et al., 2024). Such divergence can be largely attributed to the contribution of HMS formed in cloud/fog processes, as evidenced by a previous study reporting comparable levels of HMS (<1 µgm-3) in Beijing to this work in the absence of cloud/fog, while peak HMS levels of 18.5 µgm-3 were observed during fog processes (Ma et al., 2020). During our sampling period in Nanjing, there were no prolonged fog events (RH>90 % and visibility < 1 km) lasting over 2 h (Fig. S2e). Additionally, a previous study has emphasized that although in-cloud formation processes can be much faster compared with aerosol water, given its large water content, their contribution to the near-surface aerosol composition can be negligible during China's winter haze, due to the accompanied temperature inversions and high atmospheric stability, so that the weak vertical exchange impeded the transportation of gas precursors emitted near the surface to high altitudes and the chemicals produced in the high-altitude cloud could not be easily transported to the ground (Wang et al., 2022b). Here, we utilized the vertical temperature profiles retrieved from http://weather.uwyo.edu/upperair/sounding.shtml (last access: 10 June 2025) to identify temperature inversion within the atmospheric boundary layer in the winter of Nanjing. As shown in Fig. S3 in the Supplement, a predominant occurrence of temperature inversions was noted across our observation days, characterized by inversion layers extending from the surface to altitudes of 2000 m, particularly evident on hazy days. Furthermore, days lacking temperature inversions (from 19 to 25 December 2023) were associated with negligible cloud water content (Fig. S2f), which were obtained from MERRA-2 (Modern-Era Retrospective Analysis for Research and Applications, Version 2; Gelaro et al., 2017). In line with Ma et al. (2020), we also detected HMS within PM2.5 samples during seven non-cloud days. Therefore, given the protective effects of temperature inversion and low wind speeds (Fig. S2a), as well as reduced cloud water content prevalent during our observations, the contribution of in-cloud/fog HMS formation to observed particulate HMS levels was probably insignificant and the notably lower HMS levels further suggest that the aerosol bulk water might have served as a predominant medium for HMS formation during our observations.

Other factors, such as the levels of precursors and atmospheric oxidants, may also contribute to this divergence. For instance, during the winter haze in Beijing, the average levels of HMS and sulfate were reported to be 4 and 45 µgm-3, respectively, with HMS/sulfate of 10 %, and the gaseous SO2 and HCHO concentrations were recorded at 12 and 20 ppb, respectively (Ma et al., 2020). This study observed significantly lower levels of SO2 (2.2 ± 0.7 ppb) and HCHO (5.4 ± 1.1 ppb) during the haze event. Conversely, the reduced HMS/sulfate ratio could be elucidated by the higher O3 level in this work (43.3 ± 4.7 ppb), compared with Beijing (5 ppb), as low atmospheric oxidation levels could encourage more SO2 to participate in the formation of HMS rather than sulfate (Song et al., 2019; Ma et al., 2020; Campbell et al., 2022).

In addition, the SO2 concentration exhibited minimal variation throughout the entire sampling period, while the HCHO concentration (ranging from 0.88 to 7.11 ppb where data are available) increased during PM2.5 pollution episodes (Fig. b). HMS levels strongly correlated with HCHO, with a Pearson correlation coefficient, R, of 0.61, but showed no correlation with SO2 (Fig. S4 in the Supplement). However, peaks in HCHO level did not consistently coincide with peaks in HMS concentration, suggesting that other factors beyond these specific precursors, such as meteorological conditions and aerosol physicochemical properties, might exert a more significant influence on HMS formation (Campbell et al., 2022). Thus, correlation analysis between HMS levels and other factors, including PM compositions and gas pollutants, as well as meteorological conditions, were conducted, in order to delve deeper into the potential drivers behind HMS formation in the winter in Nanjing (Fig. S4). The HMS concentration exhibited strong correlations with sulfate and PM2.5 level, with values of R of 0.87 and 0.67, respectively. The strong HMS-sulfate correlation can be partially explained by the concurrent generation of HMS and sulfate, given that both species were primarily formed through aqueous-phase S(IV) chemistry. A prior study has highlighted a strong correlation between HMS concentration and organic aerosol (OA) in Fairbanks, USA, where OA can dominate the ALWC, due to its substantial contribution to PM2.5 mass (up to 75 %) and moderate hygroscopicity (Campbell et al., 2022). In this work, organic aerosols were also identified as crucial components in both urban and marine aerosols (Fig. S5 in the Supplement). In urban aerosols, organic aerosol mass (OA = 1.6 × OC; Turpin and Lim, 2001) contributed between 10.4 % and 43.6 % to PM2.5, where water-soluble organic carbon (WSOC) accounted for an average of 62 %. For marine aerosols, the contribution of organic OA stood at 21.4 ± 6.4 %, with nearly two-thirds constituting WSOC species. Organic components in urban aerosols, particularly WSOC, also exhibited a strong correlation with sulfate and HMS levels in our observations (Fig. S4), probably indicating their possible involvement in aqueous sulfur chemistry processes.

Here, notable correlations (R = 0.75) between HMS levels and RH (ranging from 37 % to 87 %) were observed, aligning with prior research, as elevated humidity can enhance the particle water uptake and subsequent gas dissolution. Additionally, HMS levels exhibited a significant correlation with temperature (R = 0.60), contrary to findings in Fairbanks, USA (Campbell et al., 2022), where lower temperatures were linked to enhanced solubility of SO2 and HCHO, thereby facilitating HMS formation. It can be explained that, in this study, higher temperatures were generally observed during haze days, typically associated with conditions favoring HMS formation, such as increased humidity and HCHO levels (Fig. ), ultimately resulting in a positive correlation between HMS concentration and temperature. Furthermore, no significant correlation was found between HMS and wind speed (WS). The backward trajectory analysis also indicated that the air masses during haze episode predominantly originated from proximate regions (75 %), while a minor proportion (25 %) was transported from the eastern marine area (Fig. S6 in the Supplement). Collectively, these findings might suggest that observed particulate HMS levels in Nanjing are largely formed on-site in aerosol aqueous water, rather than being transported after its formation.

Therefore, the role of aerosol properties in HMS formation was further evaluated based on ALWC, pH, and ionic strength (IS) estimates from thermodynamic models (Fig. S7 in the Supplement). For urban aerosols, the estimated ALWC ranged from 4.5 to 144.9 µgm-3 throughout the entire observation period, with elevated ALWC levels during haze pollution, averaging at 84.5 ± 38.4 µgm-3 (Fig. , Table S1). The variations in ALWC could be explained by the differences in RH and aerosol compositions, as indicated by their strong correlations. The range of aerosol pH estimates fell between 3.2 and 5.8, a range known to be favorable for HMS formation (Song et al., 2019, 2021; Moch et al., 2020). Notably, during haze pollution, the aerosol pH levels were estimated to be a half-unit lower (4.7 ± 0.5) than those on clean days (5.2 ± 0.4; Fig. ). This trend has been reported in Nanjing (Sha et al., 2019) and other regions, such as Beijing (Ruan et al., 2022) and Sichuan Basin (Fu et al., 2024), a pattern frequently linked to enhanced sulfuric acid and nitric acid formation. The RH conditions and sulfate levels were identified as pivotal factors influencing pH fluctuations in this study, based on a random forest model combined with Shapley additive explanations (SHAP) analysis (Zhang et al., 2025; as detailed in Sect. S4). We also estimated the aerosol ionic strength, ranging from 5.6 to 16.8 molkg-1, falling within the typical IS range for continental aerosols (Herrmann et al., 2015). Consistent with prior research (Song et al., 2018), we noted higher ionic strengths under lower humidity conditions. A pronounced negative correlation between IS and RH (R = -0.89) was identified, even in situations characterized by heightened PM2.5 levels (Fig. a), which can be attributed to the fact that, under high humidity conditions, an increased formation of hygroscopic species can ultimately lead to a more diluted aerosol bulk solution. Specifically, with RH increasing by 10 %, the aerosol ionic strength can decrease by around 2 units. This phenomenon accounted for the lower IS levels observed during pollution events (8.8 ± 2.1 molkg-1, 74 ± 8 %), compared with the dry and clean days before (12.9 ± 3.3 molkg-1, 52 ± 17 %). While acknowledging that the regression between RH and IS may not be universally generalizable to other regions, our findings are consistent with earlier field and model research indicating a decline in aqueous ionic concentrations on humid haze days, due to the rapid rise in ALWC (Song et al., 2018; Shen et al., 2024a; Wang et al., 2024).

HMS levels displayed a notably positive correlation with ALWC (R = 0.67), in agreement with prior studies (Ma et al., 2020; Campbell et al., 2022), but demonstrated an inverse relationship with pH variations and were negatively correlated with ionic strength. The inverse relation between HMS level and pH has been reported in previous studies (Scheinhardt et al., 2014; Zhang et al., 2024) but not fully explained, as it contrasted with the established HMS formation chemistry, where the HMS formation rates (PHMS) can decrease, theoretically, by 10 to 100 times with 1-unit reduction in aerosol pH. Moreover, the negative correlation with ionic strength appeared to contradict earlier laboratory investigations that showed a continuous increase in reaction rate constants for Reactions () and () with rising IS, from <1 molkg-1 (mimicking cloud/fog conditions) to 11 molkg-1 (mimicking urban aerosol conditions; Zhang et al., 2023). This could be explained by dual impacts of ionic strength, which can not only enhance the reaction rate constants for Reactions () and () (Zhang et al., 2023) but also hinder the solubility of SO2 and influence the dissociation constants of H2SO3 (Millero et al., 1989; Fig. S8 in the Supplement). Here, the IS-dependent influence on the HMS formation rate was characterized in terms of an enhancement factor (EF), calculated as EF = PHMS/PHMS, dilute. The value of PHMS, dilute was calculated using the classical parameters obtained in dilute solution (i.e., IS < 1 molkg-1), mimicking the condition of cloud/fog droplets (Seinfeld and Pandis, 2016). Thus, EF > 1 indicated that the ionic strength level resulted in a faster HMS formation rate compared with that within cloud/fog droplets. As shown in Fig. b, the IS-dependent enhancement on PHMS exhibited a discontinuous response to variations in IS, showcasing peak enhancement at an IS of approximately 4 molkg-1 with EF > 3000 at pH of 4, beyond which the EF gradually diminished. However, when IS surpassed 16.5 molkg-1, the EF dropped below 1.0, indicating that higher ISs may hinder, rather than promote, HMS formation. In urban Nanjing, the aerosol ionic strength (6–20 molkg-1) fell in the range where increasing IS level impeded HMS formation and every 2-unit reduction in ionic strength resulted from an 10 % increase of humidity level, which in turn accelerated the PHMS by around 10 times and also explained the observed negative correlation between HMS level and aerosol IS (R = -0.62).

The daily averaged steady-state PHMS throughout the sampling period in Nanjing was further determined (as detailed in Sect. S5) to explore the potential role of aerosol properties, such as acidity and ionic strength, in ambient HMS formation. Given that carbon monoxide (CO) was usually considered to be an inert chemical species during rapid haze formation, with its increase often interpreted as indicative of the accumulation of primary pollutants in the shallower boundary layer (Williams et al., 2016), the ratio of HMS to CO (HMS/CO) was calculated, to better represent the secondary formation of ambient HMS (Fig. f). During our study period, enhanced HMS formation was noted during hazy days, as evident by the higher HMS/CO ratio (0.51 ± 0.11). The PHMS estimates exhibited a good correlation with HMS/CO (R = 0.57; Fig. S9a) and could roughly capture the diurnal variations of HMS/CO during pollution periods. Besides, elevated HMS formation rates were found during haze events, with averaged PHMS of 5.8 ± 5.9 × 10⁻³ µgm-3h-1, an order of magnitude higher than that during the clean periods (4.5 ± 8.4 × 10⁻⁴ µgm-3h-1; Fig. f). Certainly, when the ionic strength effect in aerosol water was not considered, daily PHMS was generally calculated to be 1 to 2 orders of magnitude lower (Fig. S9b). Notably, even with a 4-fold increase in ALWC coupled with a 2-fold increase in HCHO levels, these factors cannot completely counterbalance the potential 10-fold reduction in HMS formation rates resulting from the decreased aerosol pH, leading to slower HMS formation rates (1.2 ± 1.7 × 10⁻⁴ µgm-3h-1) during hazy days, compared with clean days (3.3 ± 5.3 × 10⁻⁴ µgm-3h-1; Fig. S9c), and failing to explain the higher HMS/CO ratios and HMS levels. Similar discrepancies have also been highlighted in previous studies where estimated HMS formation rates, without the consideration of high IS levels in aerosol water, inadequately represented the ambient HMS concentrations and their temporal fluctuations (Ma et al., 2020; Campbell et al., 2022; Zhao et al., 2024). For instance, a prior study has reported a PHMS of 2.6 × 10⁻² µgm-3h-1, which was estimated using parameters (i.e., SO2 solubility, k1, and k2) obtained in dilute solution and thus failed to represent the significant HMS levels in Beijing (up to 18.5 µgm-3; Ma et al., 2020). These results raised a possibility that the HMS formation rate could be largely underestimated without considering high ionic strengths in aerosol water. During our observation, we found that it was the reduction in aerosol ionic strength on humid and polluted days that led to more pronounced enhancement in HMS formation. This ultimately led to a nearly 10-fold rise in PHMS during haze episodes, compared with dry and clean days (Fig. S9d), contributing to the elevated HMS level and HMS/CO ratio during haze events.

It was noted that the IS-dependent impacts on SO2 solubility and H2SO3 dissociation constants were only measured up to 6 molkg-1 and that the effects beyond this range were extrapolated based on established relationships from experimental data (Millero et al., 1989). Building upon these extrapolations, Zhang et al. (2023) further refined the relationship between IS (<11 molkg-1) and k1 and k2, based on laboratory-measured HMS formation rates, which already accounted for the potential uncertainties inherent in these extrapolation results for IS, ranging from 6 to 11 molkg-1. Consequently, it was expected that the EF calculations can effectively represent the IS effect on HMS formation rates for ISs below 11 molkg-1. However, uncertainties in EF determination at high IS levels (>11 molkg-1) may persist, potentially contributing to the notably lower PHMS predicted under high IS conditions, particularly on clean days with lower RH conditions. In addition, while aerosol HMS formation was typically thought to take place within the bulk aerosol water, the distinct characteristics of aerosol surfaces, such as a high surface-to-volume ratio or a complex and concentrated species distribution, can potentially boost the uptake of SO2 and HCHO and thus facilitate the HMS formation process. For instance, the complex products involving HCHO with H2O (Ervens et al., 2003) and HMS with SO32- (Ota and Richmond, 2012), formed near or at the aerosol surface, may enhance the conversion of gas-phase precursors to aqueous phase. These processes may also contribute to the disparities between the lower HMS formation rates and ambient HMS levels. Besides, the aforementioned IS-dependent effects were determined for a well-mixed binary aqueous system containing Na+ and Cl- or NO3-, which may also introduce inaccuracies when applied to ambient aerosols. Ambient aerosols contain both water-soluble inorganic and organic compounds, together with water-insoluble organic compounds, potentially undergoing phase separation, which may lead to two distinct phases: an inorganic-rich hydrophilic phase and an organic-rich hydrophobic phase. Given that the formation of HMS necessitates the initial hydration of SO2 succeeded by the acidic dissociation of H2SO3 into HSO3- and SO32-, it is likely that the HMS formation predominantly proceeds within the water-rich fraction and that separated liquid phases could have differing properties (i.e., pH and ionic strength), thereby influencing the HMS formation process. Additionally, the concentrated inorganic ions in aerosol water (i.e., SO42-, NO3-, Cl-) can largely enhance the partitioning of gas-phase HCHO compared with pure water, due to the “salting-in” effect, with effective Henry's law coefficients for HCHO being 10²–10⁴ times higher than the classical value reported for pure water (Shen et al., 2024a; Zhao et al., 2024). A recent field-based study tried to formulate the effect of aqueous sulfate concentration (Csulfate, in moles per kilogram ALWC) and the effective Henry's law coefficients for HCHO. They found that while HCHO solubility did increase with rising Csulfate levels, ranging from 1 to 9 molkg-1 ALWC in the winter of Beijing, hazy days experienced significantly lower HCHO solubility by 1–2 orders of magnitude, due to lower Csulfate values, as a result of rapid increase in ALWC. In this study, we also observed lower Csulfate levels but still estimated higher PHMS during haze events (Fig. S10 in the Supplement), further indicating the important role of ionic strength in promoting the formation and accumulation of HMS. Overall, the values of PHMS reported here only serve as a first approximation to describe the potential daily fluctuations of HMS formation rates; further laboratory experiments conducted under more atmospherically relevant conditions (i.e., IS > 11 molkg-1, various aerosol compositions, and aerosol-phase states) are recommended, to better refine our understanding of the impacts of ionic strength on particular sulfur chemistry.

More importantly, our results demonstrate that the discontinuous nature of IS-dependent enhancement on HMS formation allowed the reduced IS levels observed during humid and hazy days to effectively offset the inhibitory impact resulting from a half-unit decrease in aerosol pH, consequently resulting in enhanced HMS formation. This also explains the negative correlation between aerosol IS and HMS level. In a previous study, it has also been noticed that incorporating the IS effect in regional models might occasionally boost HMS formation, even under lower aerosol water content and elevated aerosol acidity conditions in urban Beijing, whereas the exact extent and scope of these compensatory mechanisms remain ambiguous.

Sensitivity tests further revealed that a 10 % decrease in aerosol acidity and ionic strength exerted notably stronger and adverse effects on HMS production rate, compared with other factors, including ALWC, gas precursor level, and temperature (Fig. a). Given the commonly observed heightened humidity conditions and resultant lower ionic strength, as well as the reduction in aerosol acidity during winter haze, the interaction between aerosol acidity and ionic strength on HMS formation rates was preliminarily quantified by analyzing PHMS isopleths as a function of pH and IS levels in different environmental conditions (Fig. b–d). Here, the averaged conditions from different environments (i.e., urban haze, urban clean, and marine atmospheres), as detailed in Table S1, were utilized in the PHMS calculations. The dashed green lines, denoted EF = 1, represented the point at which PHMS was equivalent to PHMS, dilution, estimated for a dilute solution, mimicking conditions of cloud/fog droplets (IS < 1 molkg-1). As depicted by the green lines, pH-dependent promotion in PHMS intensified at elevated pH levels. For instance, PHMS at pH 4 was approximately 30 times faster than at pH 3, and PHMS at pH 6 was over 100 times faster than at pH 5. This dashed green line also exhibited a declining trend with increasing pH, suggesting that ionic strength played a more pronounced role in facilitating HMS formation within highly acidified aerosols. Furthermore, the red ridgelines at IS ≈ 4 molkg-1, which represent the IS level associated with the highest PHMS at a given pH, can divide the figure into two regions. Above the ridgelines, a pH-limited regime can be identified, where HMS production rate escalated with increasing pH but diminished with rising IS levels. Conversely, below the ridgelines, a probable co-limited regime emerged, where PHMS rose with both IS and pH levels, with changes amplified by variations in both factors. It is noted that there is consistent positioning of ridgelines across Fig. b–d, suggesting that the variations in other factors, such as precursor concentrations and ALWC, exhibit minimal impact on regulating HMS formation, compared with aerosol pH and ionic strength. In addition, we found that PHMS at the ridgelines was larger than that under 1-unit higher pH at dashed green lines. These results imply that the enhancement of aerosol ionic strength level can potentially offset the inhibitory effects of more than 1-unit decrease in aqueous pH, highlighting the importance of HMS formation in aerosol water, compared with dilute solutions. In this study, urban aerosols predominantly fell within the pH-limited zone, given that their higher IS levels resulted from the prevalence of ionic species and moderate humidity conditions (Fig. b and d). Therefore, although aerosol pH declined during haze days (red dots in Fig. b), the enhancement from lower IS levels under higher humidity conditions ultimately led to higher HMS formation rates than clean days (pink dots in Fig. d).

Additionally, particulate sulfur chemistry, including HMS formation, has been demonstrated in coastal and marine regions (Hong et al., 2023; Zhao et al., 2024), where aerosols probably exhibited lower IS levels in comparison with continental areas, owing to the moist and pristine atmospheric conditions (Song et al., 2018). In light of this, here we also estimated the aerosol properties and the potential HMS formation rates in marine atmosphere during the cruises in YS and BS. High humidity conditions were observed, with an average value of 83 % ± 6 % (Fig. ). Chemical analysis of cruise samples revealed that the ambient concentrations of SO2(g), HMS, and sulfate averaged at 0.82 ± 0.47 ppb, 0.05 ± 0.01 µgm-3, and 2.30 ± 0.40 µgm-3, respectively. The estimated average characteristics of the marine aerosols included an ALWC of 14.7 ± 6.40 µgm-3, a pH of 4.25 ± 0.15, and an ionic strength of 4.30 ± 1.25 molkg-1 (Table S1, Fig. S11 in the Supplement). Notably, these marine aerosols resided in the region near the ridgeline (Fig. c), where the ionic strength ranges exhibited more significant enhancements on HMS formation, compared with urban aerosols. In this zone, the rate of HMS formation, when factoring in the IS effect, typically surpassed that under dilute solutions, where the pH was 1 unit higher (dashed green line). This might imply the potential importance of HMS formation in ambient aerosol even amid the rapid acidification of sea salt particles due to IS-dependent enhancement. Using the averaged [SO2(g)] = 0.82 ppb and [HCHO(g)] = 0.5 ppb (Ervens et al., 2003; Zhao et al., 2024), the potential HMS formation rates in these marine aerosols were calculated to be 2.06 × 10⁻⁵ µgm-3h-1, a value comparable to the cloud/fog-based HMS production rate (1.2 × 10⁻⁵ µgm-3h-1) reported near the Beaufort Sea (Liu et al., 2021a), with a liquid water content (LWC) of 4.8 mgm-3 and a pH of 5. Considering the minimal impact of temperature inversion during our observation in April, here we also determined the in-cloud HMS formation rate to be 4.95 × 10⁻⁵ µgm-3h-1 in our marine environment, using a LWC of 4.8 mg m⁻³ and a pH of 5. These results further highlight the significance of IS-dependent enhancement in HMS formation, which can render the HMS formation within aerosol water a process comparable to that observed in cloud and fog environments, particularly in humid and pristine conditions.

It is logical to see lower HMS production rates in marine aerosol compared with continental aerosols, given the lower levels of gas-phase precursors, heightened aerosol acidity, and reduced aerosol water content. These factors collectively lead to significantly diminished levels of aqueous-phase precursors, resulting in a lower formation rate. Therefore, we calculated the aqueous HMS conversion ratio by normalizing the HMS level against the stable aqueous concentration of SO2 ([SO2(aq)]; as shown in Eq. S7 in the Supplement), while factoring in the influences from variation in gas-phase level, aerosol water content, and acidity, to assess the role of IS on HMS formation under various atmospheric conditions (Fig. S12 in the Supplement). In urban Nanjing, higher conversion ratios were observed during hazy days compared with clean days; this could probably be attributed to the impact of ionic strength, where lower IS levels exhibited more pronounced enhancement on HMS formation during haze events. Notably, despite the lower HMS and SO2(g) levels observed in marine aerosols, the aqueous conversion ratio for HMS was approximately twice as high as that in urban aerosols, potentially due to the HMS-formation favored ionic strength levels (ranging from 2.0 to 6.0 molkg-1) in marine aerosols.