Long-term observations of aerosol chemical components and precursor gases are conducted at an urban site of Changzhou Environmental Monitoring Center (31.76° N, 119.96° E), which is located in Changzhou, an important city in the center of the Yangtze River Delta (YRD) region. Further details regarding the sampling site and instrument information are described elsewhere (Li et al., 2023; Yi et al., 2022). Briefly, the PM2.5 is measured by the Continuous Particulate Matter Monitor (BAM 1020, Met One Inc., US) using β-ray technology, and the meteorological parameters are obtained from a meteorological monitor (WXT520, VAISALA Inc., FL). The water-soluble inorganic ions and the gas species, including NH3, HNO3, and HCl, are measured by a MARGA ion online analyzer (ADI2080, Metrohm Inc., CHN). Here the data from 2018 to 2023 are analyzed.

The thermodynamic model ISORROPIA v2.3 (Fountoukis and Nenes, 2007) is employed to predict the aerosol water content (AWC) and aerosol acidity, which is defined as the free molality of protons (Fountoukis and Nenes, 2007; Pye et al., 2020). Input parameters include SO42-, total nitrate (gas HNO3 + particle NO3-), total ammonia (gas NH3 + particle NH4+), total chloride (gas HCl + particle Cl-), NVCs, and meteorological parameters like the temperature T and relative humidity RH. The ISORROPIA model is run in the forward mode and a metastable state (Zheng et al., 2022b).

The ISORROPIA-predicted concentrations of NH3, NH4+ and NO3- agreed well with measurements (R2 all above 0.95 and slopes all close to 1.0; Fig. S1 in the Supplement). This demonstrates that thermodynamic analysis accurately reflects the aerosol state. However, the predicted HNO3 concentration does not correlate well with the observed concentrations, as has been observed in many other studies (Ding et al., 2019; Zhou et al., 2022). This discrepancy may be attributed to two factors: (1) the high measurement uncertainty of gas-phase HNO3 due to its low concentration and viscous properties, which may cause its adsorption on the MARGA units' inlet and tubing (Rumsey et al., 2014); and (2) the calculation accuracy of ISORROPIA thermodynamic equilibrium model, particularly in predicting activity coefficients (Zheng et al., 2022a). The influence of this discrepancy on the results in this study is tested to be small, but its influence under other scenarios needs to be examined in future studies.

Time series analysis is a statistical method of analyzing a sequence of data points over an interval of time, which is particularly useful for understanding the structure and pattern of temporal data and is widely applied in atmospheric studies (Hammer et al., 2020; Kang et al., 2020; Shumway and Stoffer, 2017). Here, we performed time series analysis of pH and its potential influencing factors by decomposing them into four components: long-term trends, seasonal variations, diurnal cycles and random residuals. Linear fitting (y=a×t+b, where t is defined as time hereinafter) is adopted to predict the long-term trends (Kang et al., 2020; Mudelsee, 2019), and one-term Fourier curve fitting (y=a0+a1×cos⁡(ωt)+b1×sin⁡(ωt)) is adopted to fit the seasonal and diurnal cycles (Bloomfield, 2004; Singh et al., 2017). Here, we fixed the cycle period of Fourier curve as 1 year and 1 d in fitting the seasonal and diurnal variations, respectively. The random residuals were obtained from the difference between the actual observed values and the sum of the predicted values of fitting functions in the long-term trend, seasonal variations and diurnal cycles. See more details in Sects. S1 and S2 in the Supplement.

To quantify the contribution of a direct influencing factor to the variations of a certain term, the one-at-a-time sensitivity analysis method is adopted (Yu et al., 2019). Briefly, assume variable Y is a function of n influencing factors of x1 to xn, i.e., Y=f(x1,⋯,xn). The variation in Y due to factor xi, ∂Y∂xi, is estimated as 1∂Y∂xi=f(x1‾,⋯,xi,⋯,xn‾)-f(x1‾,⋯,xn‾), where xi is the actual value of factor xi, and xi‾ is the average of factor xi. See more details in Sect. S3.

The recently proposed multiphase buffer theory reveals that most continental regions are within the ammonia-buffered regime, where the pH variations can be decomposed into (Zheng et al., 2020, 2022a) 2apH=pKa∗+cni+Xgp, where 2bKa∗=Ka,NH3ρwHNH3RTAWC2ccni=log⁡γH+γNH4+2dXgp=log⁡[NH3(g)][NH4+(aq)]. Here, Ka∗ is the effective acid dissociation constant of NH3 under ideal conditions in multiphase systems, cni is the non-ideality correction factor and Xgp represents the gas–particle partitioning of NH3. Ka,NH3 is the acid dissociation constant of NH3 in bulk aqueous phase, ρw is the water density, HNH3 is Henry's law constant of NH3, R is the gas constant, T is temperature in K and γX is the activity coefficient of X.

Each term of the top-level pH decompositions (Eq. 2a) further depends on many other influencing factors, making the overall picture complicated. To illustrate the interconnections among these multiple driving factors, we applied the interpretive structural modeling (ISM) approach, which is widely used to identify and analyze the relationships between factors in complex systems (Sushil, 2012; Thakkar, 2021). With this method, a hierarchical relationship among influencing factors of aerosol pH can be established based on the multiphase buffer theory, as illustrated in Fig. 1. Take pKa∗ for illustration here; other direct drivers of cni and Xgp are elaborated in Sect. S4 (Zheng et al., 2022a, 2024b). pKa∗ makes a direct impact on pH (top-level influencing factor), and its variation is determined by the temperature and AWC. The AWC further depends mainly on PM2.5 concentrations and RH and minorly on the chemical profiles (middle level). Fundamentally, these influencing factors are caused by variations in synoptic conditions and emissions (bottom level).

With the above ISM approach, a quantitative analysis of each factor following the influencing lines can be achieved. In addition, when coupled with time series analysis, it can be applied to illustrate the driving factor of each time series component. Briefly, we can decompose each input parameter in ISORROPIA v2.3 into the four time series components (Sects. 2.1 and 2.2) and then apply each component to explain upper-level factors of corresponding component. For example, the seasonal variations in Y due to seasonal variations of factor xi, ∂Y∂xiseas, is estimated as 3∂Y∂xiseas=f(x1‾,⋯,xi,seas+xi‾,⋯,xn‾)-f(x1‾,⋯,xn‾), where xi,seas is the decomposed seasonal variation in xi. See more details in Sect. S2.

The long-term pH trends in Changzhou show a slight decreasing trend of -0.05yr-1 (Fig. 2b). The top-level ISM decomposition reveals that this is due to the competing trends of pKa∗ and cni with Xgp: while pKa∗ and cni decreased by -0.12 and -0.14yr-1, respectively, the Xgp increased by 0.21 yr-1 (Fig. 3a).

A further delve into the middle-level factors in the ISM approach reveals that the pKa∗ decrease is due to the combined effect of decreasing AWC and increasing temperature (Fig. 3b). The temperature increased by 0.74 Kyr-1 (Fig. S3), corresponding to a pKa∗ of -0.05yr-1. In comparison, the AWC exhibited a decrease of -1.57µgm-3yr-1 (Fig. S3), corresponding to a pKa∗ of -0.07yr-1. The AWC decrease is primarily attributed to the PM2.5 decrease (around -1.6µgm-3yr-1), while the long-term RH shows minimal variation (Fig. 3c). As for cni, its decreasing trend is mainly attributed to increased temperature, corresponding to cni of -0.13yr-1 (Fig. 3d). RH and the fraction of NO3- in particle-phase anions (fNO3-) cause negligible effects on cni because they were nearly constant (Fig. S3). In terms of Xgp, its increase is due to the increase in both relative abundance of alkaline to acidic substances (Ct/At) and temperature (Fig. 3e), contributing to the Xgp increases of 0.16 and 0.05 yr-1, respectively. Here the temperature influences Xgp through the gas–particle partitioning volatility of semi-volatile species like ammonium nitrate. The increase in Ct/At is further due to a much larger decrease in At (sulfate, total nitrate, total chloride, etc.) than Ct (total ammonia and NVCs, etc.) (Fig. S3).

Overall, we see that the long-term pH trend shows only a slight decrease despite considerable emission changes during this period, which is a combined effect of decreased PM2.5 while increased temperature and Ct/At.

Influencing factors of seasonal variation pH are analyzed in similar ways with the long-term trends (Fig. 4). Overall, the pH is higher in winter and spring than summer and autumn, with the amplitude of seasonal variations being 0.81 or the variation range being 1.62. The extent of variation is quantified by variation range hereinafter, which is the difference between the highest and lowest values for a given variable and for a given time series component. This cycle is consistent with pKa∗ and cni, while it is in reverse phase with Xgp.

The middle-level ISM decomposition demonstrates that the seasonal variation in pKa∗ is mainly driven by the temperature (Fig. 4b). The variation in temperature is 23.26 K (Fig. S4), which corresponds to a pKa∗ variation of 1.20. In comparison, the AWC varies to a lesser extent seasonally (Fig. S4), causing a relatively minor variation of 0.42 in pKa∗. Seasonal variation in the AWC is further primarily attributed to the variation in PM2.5 levels (approximately 25.4 µgm-3), as the seasonal RH varied little (Figs. 4c and S4). As for Xgp, its seasonal variation is influenced by both temperature and Ct/At, which correspond to variations in Xgp of -0.98 and -0.91, respectively (Fig. 4d). Higher temperature and Ct/At during summer facilitate more NHx remaining in the gas phase than winter (Fig. S4). Regarding cni, its seasonal variation is attributable to the combined effects of temperature and fNO3- (Fig. 4e), leading to variations in cni of 1.25 and 0.54, respectively. Again, the influence of RH is negligible due to its little variation (Fig. 4e). The seasonal variation of fNO3- is governed by significant variations of temperature (Fig. 4f). Temperature in winter is low enough and causes the vast majority of total nitrate to partition into the particle phase, leading to minor variation in fNO3- with temperature variations (Fig. S5). Conversely, higher temperatures in summer result in more total nitrate existing as HNO3, and fNO3- is sensitive to temperature variations.

Overall, we see that the large seasonal variation in pH is mainly driven by the temperature as it plays a dominant role in pKa∗, cni and Xgp (74 %, 89 % and 52 %, respectively). In comparison, the net influence of chemical profiles is relatively smaller, contributing 48 % and 10 % to Xgp and cni, respectively. That is, the seasonal variation in pH is largely driven by the meteorology (especially temperature) rather than emissions.

Diurnal cycles of pH are higher at nighttime than daytime, with a variation range of 0.65. Similar to the seasonal variations, the diurnal cycle is also consistent with pKa∗ and cni trend, while it is in a reverse trend with Xgp (Fig. S6a), with their contribution to pH being 0.70, 0.58 and -0.63, respectively.

The major driving factor of diurnal cycles in pKa∗ is different to that of seasonal variations. First, the diurnal cycle of pKa∗ is driven by both the AWC (0.45) and temperature (0.25) (Fig. S6b), in contrast to the dominance of temperature in seasonal variations (Sect. 4.2). This is mainly due to the much smaller temperature variation range diurnally (4.87 K; Fig. S7) than seasonally (23.26 K). In addition, diurnal variation in the AWC is primarily influenced by RH (Fig. S6c) due to the larger RH diurnal variations (16 % versus 3 % in seasonal variations; Figs. S7 and S4), in contrast with the PM2.5 dominance in seasonal variations. In terms of Xgp, its dominant driving factor of diurnal cycles is Ct/At, in contrast with the dominance of temperature in seasonal variations (Fig. S6d). Diurnal cycles of cni are due to the combined effects of temperature and fNO3- (Fig. S6e), where fNO3- is further mainly driven by chemical profiles (Fig. S6f).

The random residual of aerosol pH is another major contributor to pH temporal variations, which is comparable with the seasonal variations. Distinct from all the three components above, the largest top-level contributor to random residuals turns out to be cni (82 %), even exceeding that of pKa∗ (42 %), while Xgp causes a net negative effect (-24%; Fig. S8). Moreover, random fluctuations in cni are almost entirely due to variations in fNO3- (∼95%; Fig. 5a), which are primarily driven by chemical profiles (∼93%; Fig. 5b). The pKa∗ random fluctuations are mainly caused by the AWC (∼79%), which is further attributed mainly (∼60%) to PM2.5 variations (Fig. 5c and d). Random variations of Xgp are dominated by the chemical profiles, similar to diurnal cycles and long-term trend (Fig. S9). Overall, PM2.5 and chemical profiles are the major influencing factors for the random residual of pH, underscoring the prominence of emissions over meteorology.