Two home-built AQB systems (AQB no. 1 and AQB no. 2) consist of multiple sensors that monitor meteorological parameters such as temperature (T), relative humidity (RH), and pressure (P), as well as gaseous species and particulate matter (PM) with a temporal resolution of seconds as shown in Fig. 1 with sensor information summarized in Table S1. The gas sensors include five Alphasense amperometric B4 series sensors that measure CO, NO, NO₂, O_x (O3+ NO₂), and SO₂; a photo-ionization detector (PID-AH2, Alphasense) monitoring volatile organic compounds; and a non-dispersive infrared CO₂ sensor from Amphenol Advanced Sensors (T6713-5K). The PID sensor, equipped with a krypton lamp providing a photon energy of about 10.6 eV, cannot detect methane, which has a higher ionization potential of ∼ 13.7 eV (Glockler, 1926). Therefore, the data of non-methane hydrocarbons (NMHC) from TW-EPA are more comparable to PID data in our analysis. The PM sensor (OPC-N2, Alphasense), an optical particle counter, monitors the number size distribution between 0.38 and 17 µm, divided into 16 bins based on Mie scattering, with a sampling flow rate of ∼ 4 mL s⁻¹ and a refractive index of 1.5+0i. In addition, the mass concentration of PM₁, PM_2.5, and PM₁₀ could be calculated from the number size distribution, assuming a particle density of 1.65 g cm⁻³. These sensors were controlled by a small single-board computer, Raspberry Pi Zero W, at a time resolution of 3 s with data stored in a microSD card and uploaded to cloud storage via 4G LTE. The entire system is housed in a remodeled enclosure with a dimension of 25 cm × 16 cm × 8 cm (L × D × H) and has well-ventilated openings for sampling and exhaust. The sampling flow rate is primarily controlled by an installed fan at ∼ 5.6 L min⁻¹, corresponding to a residence time of approximately 34 s in the box. This configuration allows the system to effectively monitor ambient air quality independently without the need of additional inlets.

The calibration of AQB sensors was carried out by co-locating them with the TW-EPA Nanzi station (Fig. S1) in Kaohsiung, Taiwan (22°44^′12^′′ N, 120°19^′42^′′ E) from 4 to 19 February 2021. Nanzi station is situated on the roof of a 15 m high building in a well-ventilated environment. The primary gaseous components, dry PM_2.5 and PM₁₀ concentrations, and basic meteorological parameters are continuously monitored using standard instruments, as summarized in Table S1. For electrochemical sensors in AQB, the performance can be influenced by environmental parameters such as temperature, relative humidity, and other chemical species that have high cross sensitivity (Concas et al., 2021; Karagulian et al., 2019; Mead et al., 2013). Therefore, in this study, a linear regression with a multivariate function of voltage and the environmental temperature was applied to retrieve concentrations for gas species. For PM, the reported values by beta attenuation mass monitor (BAM) in the TW-EPA station reflect the dry-state PM concentration by controlling the measurement at RH less than 50 % (i.e., a heating device applied to reduce the sampling flow to 35 % water saturation when the ambient RH is > 50 %). On the contrary, the optical particle counter (OPC) in AQB directly monitors ambient PM concentration. The difference between BAM and OPC data reflects the amount of liquid water content in ambient conditions. A simple linear regression between them might not completely reveal the influence of hygroscopicity. Therefore, the κ-Köhler equation (Petters and Kreidenweis, 2007) was applied to derive the κ as discussed in the following section.

To bridge the PM concentration gap between BAM and OPC, the sensitivity correction of OPC and the conversion of ambient particles to dry particles are required. The sensitivity coefficient (α) was evaluated as the mass concentration ratio of BAM and OPC data at low RH (≤50 %) having limited water content, as follows: 1α=MBAMMOPC, where MBAM andMOPC are PM mass concentrations (µg m⁻³) measured by BAM and OPC, respectively. RH ≤ 50 % was applied as the threshold criteria for data selection to determine α, as the mass concentration of ambient particles might have significant water uptake at higher RH. The statistical distribution of MBAM to MOPC ratios at RH ≤ 50 % was analyzed to assign α as the mean value ± 0.5σ (σ: standard deviation) to prevent high-concentration data points from dominating the statistical result.

The particle size growth with the water saturation ratio (S) for a given κ can be evaluated using κ-Köhler equation as follows (Petters and Kreidenweis, 2007): 2S=Damb3-Dd3Damb3-Dd31-κexp⁡4σs/aMwRTρwDamb, where Damb and Dd are the diameters (m) of the ambient and dry particulate matter, respectively; σs/a is the surface tension of the particle (J m⁻²); Mw is the molecular weight of water (g mol⁻¹); R is the gas constant (J mol⁻¹ K⁻¹); T is the temperature; and ρw is the density of liquid water (1.0 g cm⁻³). The first term is the solute effect, while the second is the Kelvin effect. As the mass is dominated by the larger particles, the Kelvin effect in Eq. (2) is assumed to be negligible for simplification. The derived dry mass concentration (Md,derived) from the measured ambient particles from OPC data can be expressed as follows (Pope et al., 2010; Crilley et al., 2018): 3Md,derived=(α×MOPC)×Sκ1-S×ρwρd+1-1, where ρd is the density of dry aerosol particles and is assumed to be 1.20 g cm⁻³ in this study. With the determined α values (Eq. 1), κ can be derived from the data points of aqueous particles at RH above 70 %, and the deliquescence RH (DRH) can be verified using ion chromatography (IC) analyzed composition with the Extended Aerosol Inorganics Model (E-AIM) model. The mean absolute percentage error (MAPE) parameter between Md,derived and MBAM was used to assess the appropriate κ value as follows: 4MAPE=∑i=1nMd,derived,i-MBAM,iMBAM,in×100%, where n is the total number of data points. With the restricted range of α, κ can be derived under the minimum MAPE. The detailed process description for κ derivation is provided in the Supplement. Due to the heterogeneity between particles, PM₁₀ was divided into integrated fine particles (Dp≤2.5 µm) and coarse particles (2.5 µm <Dp≤10 µm) to evaluate the individual sensitivity coefficient and hygroscopicity.

Hygroscopicity can also be determined using the volume fraction of the major components. Based on an earlier field campaign, the ion chromatography (IC) method was applied to quantify water-soluble components for samples (both PM_2.5 and PM₁₀) collected at Fooyin University (22°36^′09.8^′′ N, 120°23^′23.1^′′ E) in Kaohsiung from 15 to 28 January 2013. Ambient aerosol samples were collected using a pair of dichotomous aerosol samplers (model RP-2025, R&P Co., Inc., Albany, New York) to collect integrated fine and coarse particles on Teflon filters with sampling flow rates of 15.0 and 16.7 L min⁻¹, respectively. The samples were categorized into daytime and nighttime. Daytime samples were collected from 08:00 to 20:00 LT, and nighttime samples were collected from 20:00 to 08:00 LT the next day. The samplers were equipped with Teflon filters deployed for the measurement of water-soluble ions (Na⁺, Mg²⁺, K⁺, Ca²⁺, NH4+, Cl⁻, SO42-, and NO3-) via ion chromatography (model ICS-1000, Dionex). More information on the chemical analysis method can be found in Salvador and Chou (2014).

To derive the hygroscopicity from samplings, the ions from IC analysis were converted to chemical components via the following sequence: ammonium sulfate, ammonium bisulfate, ammonium nitrate (when there is residual ammonium), sodium nitrate, and sodium chloride. With the assumption of the hygroscopicity of insoluble components as zero and negligible residual ion contribution (less than 5 % of total mass), the overall hygroscopicity can be derived by the volume fraction (εi) weighted hygroscopicity from individual soluble component (i species) as follows: 5κ=∑iεiκi=∑ivivtotalκi, where κi is the hygroscopicity of i species, vtotal is the volume of particles, and vi is the volume of i species. The conversion of particle mass to volume is based on a density of 1.20 g cm⁻³. The applied hygroscopicity, molecular weight, and density for the related chemical species are summarized in Table S2. With the assumption that these ions dissolve completely in the aqueous phase, which represents the maximum estimation, the hygroscopicity contributed by the residual ions were found to be approximately up to 1.8 % and 6.4 % of the overall κ value for integrated fine particles (PM_2.5) and coarse particles (PM_2.5−10), respectively. Given their limited impact on the hygroscopic behavior of the particles, the contribution of the residual ions was not taken into account in the calculation. Additionally, other PM_2.5 IC data for samples collected at the National Kaohsiung University of Science and Technology (22°46^′22.4^′′ N, 120°24^′03.4^′′ E) in Kaohsiung for the period of 8–18 December 2021 samples were also applied for further comparison (no PM₁₀ collection for that campaign). We opted for the 2013 dataset for more discussion due to its comprehensive analysis encompassing both PM_2.5 and PM_2.5−10. Furthermore, the composition data obtained from IC analysis was applied to E-AIM Model III (for systems containing H⁺, NH4+, Na⁺, SO42, NO3-, Cl⁻, and H₂O) to evaluate the characteristics of volume variation as a function of RH in the range of 30 % to 90 % (Clegg et al., 1998). The partitioning of selected trace gases (HNO₃, HCl, NH₃, and H₂SO₄) into the vapor phase was disabled to keep a consistent quantity of applied chemical species in the particle phase. The growth factor, Vamb/Vd, above DRH, was applied to retrieve the κ value using Eq. (2) but without the Kelvin effect term (Luo et al., 2020). Both the individual sample concentrations and the overall averaged composition conditions were analyzed to evaluate the hygroscopic behavior of the particles.

Figure 2 shows the time series of the meteorological parameters and pollutant concentrations between calibrated AQB and TW-EPA data from 14 to 17 February 2021. T, RH, CO, and O_x showed a good correlation with r>0.9, while NO, NO₂, PM_2.5, and PM₁₀ had a moderate correlation (r≥0.48). The high correlation (r=0.976) for CO (with a lifetime of ∼ 2 months) indicates a similar air parcel sampled by both AQB and the instrumentation in TW-EPA. The PID sensor had consistent peaks with high NMHC concentrations and could not reveal temporal variation at low concentrations, resulting in a low correlation. Overall, the AQB system performs well in capturing the ambient variability of pollutants stated above. The low correlation of SO₂ was due to the cross sensitivity of this SO₂ sensor, which was highly sensitive to O₃ and NO₂ (about -120 % reported in the technical specifications of Alphasense). O₃ and NO₂ generally have higher concentrations than SO₂ and cause a significant contribution to the response of the SO₂ sensor. However, if high-SO₂-concentration events occur, the SO₂ sensor might reflect the variation in SO₂ concentration. The PM concentration shown in Fig. 2 was calibrated using a simple linear regression, which roughly reflects the trend of mass concentration but shows more significant deviations at higher RH due to more water uptake in particles, as discussed in Sect. 3.2. Most gas species showed a high correlation (r≥0.95) between different AQB systems except for NMHC (r=0.675) as summarized in Table S3. Further results and discussions focus on the PM analysis using AQB no. 1, which has a more consistent sampling rate during the observation period, unless stated otherwise.

For simplicity, κ was derived from OPC and BAM data without considering the Kelvin effect and under an assumed particle density. Neglecting the Kelvin effect may result in minor differences for particles larger than 100 nm under sub-saturated conditions (Pope et al., 2010; Topping et al., 2005; Crilley et al., 2018). To confirm the appropriateness, we assessed biases for particles at 0.1 and 1 µm without considering the Kelvin effect, as shown in Fig. S8. For particles with a κ value of 0.3 under RH ranging from 70 % to 95 %, the deviation of κ due to neglecting the Kelvin effect is -10 % for 0.1 µm particles and -1 % for 1 µm particles, decreasing with particle diameter. The particle diameter is overestimated under the same RH conditions because the positive Kelvin effect is ignored. To compensate for the deficiency in saturation, the balanced particle diameter needs to be larger with a more significant solute effect. However, the average mass-weighted mean diameter for PM_2.5 is about 1.3 µm. Therefore, neglecting the Kelvin effect in our analysis has limited influence on the derived κ.

Furthermore, the derived κ from OPC data (using Eq. 3) and IC data (using Eq. 5) are notably influenced by the assumed particle density. Assuming that the undetermined composition mainly consists of secondary organic species with a density of 1.2 g cm⁻³, within the reported densities ranging from 0.9 to 1.6 g cm⁻³ depending on the formation process (Malloy et al., 2009; Kostenidou et al., 2007; Zelenyuk et al., 2008), along with the properties of analyzed soluble chemical species summarized in Table S2, the calculated densities are 1.42 ± 0.03 and 1.34 ± 0.05 g cm⁻³ for PM_2.5 and PM_2.5−10, respectively (Fig. S9). These calculated densities are about 15 % and 10 % higher than the assumed fixed density (1.2 g cm⁻³) for PM_2.5 and PM_2.5−10, respectively. Consequently, the derived κ from OPC data increases by approximately 17 % for PM_2.5 and 9 % for PM_2.5−10, while the derived κ from IC data is proportional to density (i.e., 15 % and 10 % for PM_2.5 and PM_2.5−10, respectively) as shown in Fig. 4b. This influence is particularly noticeable for components with a high portion of higher-density species, such as black carbon (a non-hygroscopic species with κ∼ 0) having a high density of about 1.8 g cm⁻³ (Park et al., 2004; Shiraiwa et al., 2008). Despite the potential uncertainties associated with particle density, the derived κ exhibits consistency between the OPC and IC analyses.