The field campaign was conducted at the summit of Mt. Hua (34°28′ N, 110°05′ E; 2060 m a.s.l), located in the central part of the Guanzhong Basin of western China, from 15 October to 19 November 2021. The sampling area was predominantly covered with vegetation and was distant from anthropogenic influence, with the nearest city (Huayin) being about 5.9 km away from the mountain base. Being mostly situated within the free troposphere as suggested earlier (Shen et al., 2023), this site effectively represent the free tropospheric background atmospheric conditions in this region.

A self-assembled HTDMA system was used to characterize aerosol hygroscopicity during this study. A detailed description and the working principles of the HTDMA system can be found in previous studies (Han et al., 2022; Tan et al., 2013). Specifically, the hygroscopic growth factor (GF) was measured for particles with dry diameter of 30, 60, 100, 150 and 200 nm at 90 % relative humidity (RH). The system was calibrated once a week using ammonium sulfate, which is a reference material with well-characterized hygroscopic properties.

In this study, the hygroscopicity parameter, κ, introduced by Petters and Kreidenweis as (Petters and Kreidenweis, 2007), was used to describe the hygroscopicity properties of aerosol particles based on the measured GF as: 1κ=GF3-11-RHKeKe,2Ke=exp4σs/aMwRTρwDdry, GF is the hygroscopic growth factor measured by HTDMA at 90 % RH. Ddry is defined as the particle diameter selected by the first DMA under dry conditions (RH < 10 %) at 25 °C. ρw and Mw are the density and molecular weight of water. σs/a is the surface tension of the droplets, which is assumed to be that of pure water (σs/a=0.0728 N m⁻²). R is the ideal gas constant and T is the ambient temperature, Ke is the Kelvin correction factor term. The κ probability density function (κ-PDF), indicative of a statistical distribution that describes the variation in hygroscopicity among an aerosol population, was derived from the GF probability density function (GF-PDF), which was retrieved from the measured GF distribution function (GF-MDF) using the TDMAinv algorithm (Gysel et al., 2009).

Given the complex mixing states of ambient aerosols, aerosols are commonly classified into distinct hygroscopic groups based on the hygroscopicity parameter κ (Liu et al., 2011), as more-hygroscopic aerosols normally have larger κ values and less-hygroscopic particles have smaller ones. In the present work, two different hygroscopic modes were clearly identified. Accordingly, aerosol particles were categorized into two modes with respect to their hygroscopicity: a less-hygroscopic mode (LH, κ < = 0.2) and a more-hygroscopic mode (MH, κ > 0.2), consistent with the approach of Shi et al. (2022). The values of κ for each mode were calculated as the volume-equivalent mean derived from the κ-PDF within the respective κ boundaries.

In this study, the particle number size distribution (8–750 nm) was measured using a Scanning Mobility Particle Sizer (SMPS, Model 3080, TSI Inc., USA). Water-soluble inorganic ions (Na⁺, NH4+, NO3-, SO42-) were quantified by an online ion chromatograph (online measurement-9000, Thermo Fisher Scientific, USA) through a PM_2.5 sharp-cut cyclone inlet, while the mass concentration of elemental carbon (EC) and organic carbon (OC) were determined using an OC / EC aerosol analyzer (Sunset Laboratory, Forest Grove, OR) (Bae et al., 2004).

In addition to online measurements of the particle chemical composition, offline samples were collected twice daily (07:00–19:00 and 19:00–07:00 LT the following day) on quartz fiber filters using a high-volume air sampler (TISCH, TE6070DV-BL) operating at a flow rate of 1.13 m³ min⁻¹. All collected samples were wrapped in foil and stored at ∼ 4 °C until analysis. Field blank samples were also collected before and after the sampling by mounting a prebaked blank filter onto the sampler for about 10 min without sucking any air. The major chemical components of PM_2.5, including major and trace elements as well as water-soluble ions, were subsequently analyzed using an energy-dispersive X-ray fluorescence spectrometer (ED-XRF, Epsilon 4, Malvern Panalytical, Netherlands) and ion chromatography (940 Professional IC Vario, Metrohm). Detailed information for the offline chemical analysis can be found in (Feng et al., 2023).

Meteorological conditions, including wind direction, wind speed, ambient temperature, and RH, were continuously measured from the Mt. Hua meteorological station. All the instruments for aerosol measurements were placed in an air-conditioned room, where temperature was maintained at 25 °C. The aerosol sampling inlet was located on both sides of the room. The aerosol was sampled via a low-flow PM_2.5 cyclone inlet, passed through a Nafion dryer, and directed to different instruments through stainless steel or conductive black tubing using an isokinetic flow splitter. The sampling air was dried to RH below 20 % using a Nafion diffusion dryer.

To investigate the origins of air masses reaching our observational site, the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) transport and dispersion model (Draxler and Hess, 1998) was employed. In the calculations, 72 h backwards trajectories were computed for air parcels arriving at the sampling location (2060 m a.s.l) with a temporal resolution of 2 h. This study employed the cluster analysis method proposed by Stein et al. (2015), where the clustering criterion was defined such that the spatial variance of each cluster corresponds to the sum of squared distances between individual trajectories and the mean trajectory of that cluster. The total spatial variance (TSV) was calculated as the sum of the spatial variances of all clusters. The final clustering result was obtained by minimizing the increase in TSV. The trajectory frequency distributions for the resulting clusters are provided in Fig. S8.

Figure 1 illustrates the time series of wind direction, wind speed, RH, ambient temperature, PM_2.5 concentrations, and black carbon (BC) mass concentrations throughout the entire experimental period. Overall, the average wind speed during the campaign was around 5.0 ± 3.2 m s⁻¹, with the prevailing wind directions originating from the west and northwest. The PM_2.5 mass concentration was generally below 20 µg m⁻³, with an average value of 8.2 ± 6.7 µg m⁻³, aligning with the winter 2020 averages observed at the Mt. Hua site reported by Feng et al. (2023). In contrast to the heavily polluted Guanzhong Basin urban areas, the average PM_2.5 levels were notably higher (e.g., 68.0 ± 42.8 µg m⁻³ in Xi'an; Chen et al., 2021). This discrepancy, which is consistent with previous studies (Dai et al., 2018), indicates a comparatively reduced influence of ground-level anthropogenic emissions at the current site, plausibly attributed to particle deposition or dilution during the transport from lower altitudes to the mountaintop (Feng et al., 2023). From Fig. 1, it is clearly to observe that meteorological conditions substantially changed after 6 November, characterized by a decrease in temperature, a slight increase in wind speed, and a shift in the wind direction from west to northwest. Due to the significant temperature drop during this period, domestic heating in this area was initiated. The notable differences in the meteorological conditions as well as anthropogenic emissions during the two distinct periods can result in different atmospheric processes and transport of aerosols. This would in turn lead to variations in the aerosol chemical composition as well as their physicochemical properties, in particular, aerosol hygroscopicity. Detailed analysis of aerosol hygroscopicity and their chemical composition, taking into account of the influence of air mass origins and domestic heating activities, for the two periods will be further analyzed in Sect. 3.3.

Figure 2a–e shows the temporal evolution of the κ-PDF for different particle sizes, with the black line representing the average κ. The results reveal that the average κ for particles at 30, 60, 100, 150, and 200 nm were 0.20, 0.21, 0.25, 0.27, and 0.30, respectively. Chen et al. (2021) obtained an average κ value of 0.14 ± 0.04 for the water-soluble components of 100 nm particles at the ground-level environment of the Guanzhong Basin during winter based on particle chemical composition measurements. Considering the contribution of water-insoluble components, the overall hygroscopicity would be even lower. We observed that at our observational site, water-soluble inorganic components were the dominant composition in particles (average of 77 % in mass fraction, see Fig.  2e), while the organic components contributed the most (54 % in mass fraction) at the ground-level Guanzhong Basin background site. Though bulk-phase chemical composition may deviate from that of size-resolves ones, this may partially explain the large difference in aerosol hygroscopicity between the two sites at the same region. Particles sampled at the ground level indicating the distinct sources, secondary processes for atmospheric aerosols in the free troposphere compared to ground-level environments.

The averaged κ-PDF in Fig. 3a reveals that particles of different sizes at the current study were dominated by the MH mode, indicating the aerosols at the site had a mild degree of external mixing of different sources. This characteristic is similar to the results from other high-altitude regions, which could be explained by the slight influence of the advection of aerosols from the PBL (Van Dingenen et al., 2005; Holmgren et al., 2014; Sjogren et al., 2008). As illustrated in Fig. 3a, the contribution of the MH mode becomes more pronounced as particle size increases, which means nucleation and Aitken mode particles (diameter at 30 and 60 nm) tend to contain higher number fraction of LH mode particles (see Table 1). Nucleation and Aitken mode particles are typically from new particle formation (NPF) and subsequent growth or anthropogenic sources injected from the PBL. However, NPF events were rarely observed (only once) at the current site during this study, suggesting anthropogenic emissions within the PBL were the primary sources for these smaller, less hygroscopic particles. This finding on the other hand suggests that the larger particles (e.g., 100–200 nm) at the site, characterized by a higher degree of internal mixing, may stem from different origins and are most likely subject to long-range transport with extensive aging processes. This interpretation is supported in part by Li et al. (2011), who conducted measurements during similar seasons at Mt. Hua and reported that particles in the 100–400 nm range were predominantly composed of secondary inorganic species, such as SO42-, NO3-, and NH4+, which typically have experienced longer aging processes.

No clear diurnal variation was observed in the κ-PDF of particles at most sizes at the current site, except for a minor broadening in the κ-PDF during daytime for 30 nm particles, as depicted in Fig. 3b–f. The relatively constant κ-PDF of particles at most sizes throughout the entire day is consistent with the stable diel variation in the number fraction of each hygroscopic mode and their respective hygroscopicity (see Fig. S1 in the Supplement). The wider κ-PDF for 30 nm particles during the daytime was mainly attributed to the elevated number fraction of particles in the less-hygroscopic mode. Given that our observational site is consistently located within the residual layer or the free troposphere throughout the day, the influence of vertical diffusion of pollutants from the PBL, being primarily anthropogenic, was expected to be minimal. This is particularly obvious for larger particles, which were abundant at the site, while for smaller particles, this influence became more notable due to their lower concentration that a slight vertical upward transport from the PBL may potentially alter their κ-PDF characteristics.

As aerosol hygroscopicity is ultimately determined by their chemical composition, their diurnal pattern observed aligns neatly with the daily trend in the mass fractions of each component within the particles, as shown in Fig.  S2. Note that the chemical composition data from the online measurement were used in this analysis, as the offline measurements, while having better temporal coverage, were limited to half-day resolution. Interestingly, notable differences were observed in meteorological variables, including ambient temperature and RH, as well as the concentration of atmospheric trace gases like O₃ and SO₂, between daytime and nighttime at the site (see Figs. S3 and S4). Thus, it is reasonable to expect that, during daytime, under the conditions of higher solar radiation, elevated temperatures, and increased levels of atmospheric oxidants, various secondary species are likely to form, probably through photochemical oxidation processes. These newly-formed species will subsequently partition or condense onto pre-existing particles, thereby altering their chemical composition and, consequently, their hygroscopicity. However, such an influence on aerosol chemical composition and their hygroscopicity was not observed at the current study. A plausible explanation for this could be the insignificant yield of these secondary compounds, potentially due to the scarcity of their atmospheric precursors during this season. These results further confirm that the current aerosols, particularly larger particles, were primarily originated from regional or long-range transport with longer atmospheric aging, with limited contributions from local lower altitude sources or in situ secondary formation.

Despite the absence of a clear diurnal pattern in the particle chemical composition by online analysis, semi-diurnal offline measurements demonstrated significant compositional changes between the first and second half of the campaign. Specifically, starting from 6 November, the contributions of Ca²⁺ and Fe²⁺ to PM_2.5 mass increased substantially, accounting for up to approximately 20 % of the total particle mass, indicating a shift in aerosol sources after this time. Given that Ca²⁺ and Fe²⁺ are typically recognized as mineral dust tracers (Feng et al., 2023; Kouyoumdjian and Saliba, 2006), these observations strongly suggest an episode of distinct long-range transport of mineral dust after 6 November. This signature, being consistent with previous findings (Liu et al., 2024), was further confirmed by the backward trajectory analysis as shown in Fig. 4. The results revealed that air masses arriving at the current site during this time were mainly originated from the northwest, passing through the Mongolia-Inner Mongolia corridor and Tengger Desert region at ∼ 1400 m altitude before reaching our site (Cluster 3 and 5). On the other hand, this period also coincided with the initiation of regional domestic heating, creating a unique scenario where long-range transported dust components mixed with regional emitted anthropogenic pollutants. Consequently, the arriving air masses, enriched with both mineral dust and heating-related emissions, likely modified the background aerosol chemical composition at our observational location (Du et al., 2022).

To comprehensively evaluate the impacts of long-range transport and regional emissions on aerosol hygroscopic properties, we compared the size-resolved aerosol hygroscopicity parameter (κ) across five air mass clusters identified through trajectory analysis (Fig. 5a). As Cluster 1, 2 and 4 also occurred during the latter half of the campaign, coinciding with domestic heating activities, we further divided each of these three clusters into two distinct periods. The segments during the domestic heating period of these three clusters were specifically labeled as Cluster 1 DH, Cluster 2 DH and Cluster 4 DH, where “DH” denotes the influence of domestic heating. During the first half of the campaign, which was free from significant influence of mineral dust and prior to the onset of domestic heating activities (i.e., Cluster 1, 2, and 4), aerosols exhibited clear size-dependency of κ, with κ values increasing with increasing particle size. Moreover, the κ values observed for particles of the same sizes were relatively comparable across these three clusters. Air masses associated with these clusters, particularly Cluster 1, mainly transported over relatively short distances from southeastern and southwestern regions, passing through the heavily polluted Guanzhong Plain urban agglomeration and may represent the atmospheric conditions of this regional environment. In contrast, aerosols in Cluster 3, 5 and Cluster 1 DH, 2 DH, and 4 DH displayed relatively constant κ across most particle sizes, except for sub-100 nm particles, which probably had local origins rather than long-range transport, as discussed earlier.

For 200 nm particles, Cluster 1, 2, and 4 exhibited the highest κ values (∼ 0.32), followed by Cluster 3 and 5 (∼ 0.27), while the lowest values were observed in Cluster 1 DH, 2 DH, and 4 DH (∼ 0.22). Given that the chemical composition of bulk aerosols is more representative of larger particles than smaller ones (Hong et al., 2018), this pattern was consistent with the average aerosol composition measured by the online measurements. During Cluster 1, 2, and 4, aerosols were dominated by inorganic species, such as NH4+, SO42-, NO3-, which are highly hygroscopic and accounted for over 70 % of the PM_2.5 mass fraction (see Fig. 6).

For Cluster 3 and 5, the contribution of these inorganic species decreased markedly, dropping from over 70 % to less than 50 % in mass fraction, as shown in Fig. 6. Concurrently, the levels of Ca²⁺, Fe²⁺ increased substantially, from less 1 % to approximately 20 % of PM_2.5 mass. This shift may partially explain both the reduced hygroscopicity (κ≈0.09) and the elevated number fraction (21 %) of LH mode particles in these clusters compared to those (κ≈0.12, NFLH=10 %) in Cluster 1, 2, and 4, as these mineral dust components are generally hydrophobic or weakly hygroscopic. The influence of mineral dust was further confirmed by the strong correlation between SO42- with Ca²⁺ (R2=0.83) in Cluster 3 and 5, contrasting with their weak associations (R2≈0.1) during other clusters, where SO42- was instead well linked to NH4+ (R2≈0.9) (see Fig. 7). The co-variation of SO42- and Ca²⁺ indicates that they possibly shared the same origins (Sullivan et al., 2009), with Ca²⁺ likely existing in the form of nearly non-hygroscopic CaSO₄ (κ≈0.01–0.05) during this episode, reinforcing the observed hygroscopicity decline relative to Cluster 1, 2, and 4. On the other hand, as particle size decreased, a slight increase in the overall aerosol hygroscopicity was observed in Cluster 3 and 5, which can be explained by the enhanced hygroscopicity of LH mode particles coupled with a small decrease in their number fraction. Given that mineral dust mainly resided in larger particles, this size-dependent trend in hygroscopicity suggests a reduced contribution of mineral dust to the hygroscopicity of smaller particles within Cluster 3 and 5.

As noted earlier, beginning on 6 November, which encompassed the entire duration of Cluster 3, 5, 1 DH, 2 DH, and 4 DH, regional domestic heating was initiated, which may emit substantial amounts of primary aerosols, such as black carbon (BC) and primary organic aerosols (POA). These aerosols were likely transported to our observational site via advection. This interpretation aligns with the findings of Du et al. (2022), who reported a marked increase in the fraction of organic aerosols as well as BC at Mt. Hua following the initiation of domestic heating. Though no direct source apportionment of organic aerosols can be obtained by the current study, a moderate increase (approximately 7 %) in the organic mass fraction in PM_2.5 during Cluster 3 and 5, followed by a more pronounced rise in both organic (10 %) and BC fractions (5 %) during Cluster 1 DH, 2 DH, and 4 DH was observed compared to other clusters (see Fig. 6), further supporting our previous hypothesis. Thus, the elevated levels of these primary aerosols, typically exhibited weak hygroscopicity (Shi et al., 2022), coupled with the high contents of weakly hygroscopic mineral dust, may synergistically drive the continued decline in aerosol hygroscopicity throughout this period.

Despite both being influenced by dust events and domestic heating activities, aerosols in Cluster 5 exhibited higher aerosol hygroscopicity (0.25) compared to Cluster 3 (0.23), mainly due to their larger number fraction of MH mode particles, accompanied by the higher hygroscopicity of LH mode particles, as shown in Fig. 5. Interestingly, striking high RH levels (around 80 %) were observed in Cluster 5, which nearly doubled the values in Cluster 3 (see Fig. S5). Such high-RH conditions may facilitate some specific aerosol processes, such as multi-phase or aqueous phase reactions, potentially altering their chemical composition and may explain their elevated hygroscopicity (Tong et al., 2021). This hypothesis aligns with the results of Du et al. (2022), who observed that the contribution of aqueous-formed water soluble oxidized organic aerosols to the total water-soluble organic aerosols increased from 11.21 % under low-RH levels to over 40 % at RH > 80 %, indicating a significant transformation in the organic aerosol composition. On the other hand, we noticed that the average κ of MH mode particles in Cluster 3 and 5 was markedly greater relative to other clusters (see Fig. 5). Following our preceding reasoning, we suspected that the multi-phase or aqueous phase reactions under higher-RH levels in Cluster 5, not only enhanced the hygroscopicity of LH mode particles, but also produced substantial highly hygroscopic materials, which may have persisted until the entire duration of Cluster 3 and 5. However, without detailed compositional analysis at molecular level, the exact mechanisms responsible for this exceptionally high aerosol hygroscopicity remained unclear.

In summary, during the first half of the campaign, when air masses mainly passed through the heavily polluted Guanzhong Plain urban agglomeration, aerosols were primarily composed of secondary inorganic species and exhibited the highest hygroscopicity. Starting around 6 November, increased influences from both mineral dust and domestic heating activities led to a noticeable decline in aerosol hygroscopicity, particularly in larger particles. This reduction was largely attributed to the rising levels of weakly hygroscopic components, such as mineral dust tracers (e.g., Ca²⁺, Fe²⁺), organic components as well as BC, highlighting the combined effects of long-range transport and regional emissions on aerosol composition and properties.

The unique environment of free tropospheric observation sites, being distant from anthropogenic pollution sources, provides a more representative characterization of regional-scale aerosol properties. However, current measurements of aerosol hygroscopicity in the global free troposphere are remarkably sparse (Fig. 8). These available datasets shows that hygroscopic parameter κ for free tropospheric aerosols typically ranged from 0.15 to 0.35, with ours falling within the median of reported values. Winter-time aerosols at Jungfraujoch (3580 m) revealed comparable hygroscopicity to our results, while their higher annual mean (κ≈0.3) implies substantial contribution from secondary inorganic components or more aged components during other seasons (Kammermann et al., 2010). The Monte Cimone Observatory (Italy), situated in the transition zone between the boundary layer and free troposphere, exhibited slightly reduced aerosol hygroscopicity, likely due to vertical transport of less hygroscopic pollutants, which were less-aged, from the boundary layer (Van Dingenen et al., 2005). Similarly, at lower-altitude sites, such as Huangshan (1865 m) and Puy de Dôme (1465 m), aerosol hygroscopicity was further reduced as a result of enhanced anthropogenic influence (Asmi et al., 2012; Wu et al., 2018a). These results highlight an altitude gradient in aerosol characteristics, where the influence of boundary layer decreased with elevation, resulting in progressively more aged and more hygroscopic aerosols at higher altitudes compared to fresher, less aged and less hygroscopic ones close to the surface. The Izaña Atmospheric Observatory, located in the northeastern Atlantic at 2370 m altitude, provided a different case of marine-influenced aerosol properties (Swietlicki et al., 2000). Their measurements revealed exceptionally high hygroscopicity for 50 nm particles (κ≈0.36), mostly likely stemming from the dominance of inorganic sea salts in the studied particles, contrasting markedly with continental aerosols from tropospheric sites. These comparative analyses demonstrate fundamental differences in atmospheric processes and interactions between free tropospheric and boundary layer environments by distinguishing natural background aerosol properties from anthropogenic influences, these works may establish critical benchmarks for modeling aerosol-climate interactions.