Ambient PM_2.5 (particulate matter with an aerodynamic diameter ≤ 2.5 µm) was sampled at the Chinese Research Academy of Environmental Sciences (CRAES), Beijing (40.04° N, 116.42° E). A high-volume air sampler (Tisch Environmental Inc., OH, USA) was used at an air flow rate of 1.13 m³ min⁻¹. The sampling site was situated atop a smog chamber facility (∼ 10 m above ground), with an 80 m radius free of anthropogenic emission sources nearby (Li et al., 2023b; Wang et al., 2021a; Zhang et al., 2020b). Quartz fibre filters (Pallflex™ Tissuquartz 2500QAT-UP, 8^′′ × 10^′′, Pall Corporation) were deployed for 23.5 h repeated sampling cycles, commencing at 09:00 Beijing Time (UTC+8) every day and concluding at 08:30 the following morning. Seasonal campaigns in 2023 spanned the winter period of 9–24 February, the spring period of 7 April–9 May, the summer period of 7 July–6 August, and the autumn period of 12 October–5 November. The selected four time periods are representative of the meteorological conditions and emission regimes of four quarters of the year (Li et al., 2023b; Wang et al., 2021a; Zhang et al., 2020b). The quality assurance measures for sampling filters and eligible days (Table S1) are detailed in the Supplement (Sect. S1).

The ISS method was used to measure the absorption for uncoated aerosol. Fischer (1970) first applied the integrating sphere (IS) technique to quantify aerosol absorption. Andre et al. (1981), Heintzenberg (1982), and Hitzenberger et al. (1996) subsequently combined IS with solvent systems, namely ISS, to measure aerosol absorption properties or BC concentrations. Hitzenberger and Tohno (2001) further improved the ISS system by introducing a water/isopropanol rinsing step before acetone dissolution for studies of ambient BC concentrations. After BrC was recognized as an important light-absorbing component, Wonaschütz et al. (2009) used carbon black and humic acid sodium salt as optical reference materials for BC and BrC, respectively, and established the ISS method to distinguish the absorption contributions of BC and BrC in atmospheric aerosols. Sun et al. (2017, 2021) applied the ISS method to samples from residential solid-fuel combustion in China to quantify the emission factors and light-absorption contributions of BC and BrC. More recently, Li et al. (2023b) coupled ISS with in situ PAX absorption observations to quantify differences in absorption efficiency between coated and uncoated aerosols and explicitly described the mechanism as “de-lensing through solvent dissolution and solvent de-refraction”.

As previously described, the ISS system eliminates Babs,lensing(λ) while preserving bare BC and BrC absorption components (i.e., Babs_uncoatedλ=Babs,BCλ+Babs,BrCλ) (Sun et al., 2017; Wonaschütz et al., 2009; Li et al., 2023b). The system comprises a light source, a custom-made 150 mm IS, and a UV–Vis-NIR spectrometer (Li et al., 2023b; Sun et al., 2017, 2021; Wang et al., 2021a). For each measurement, a transparent quartz cuvette (1 cm × 1 cm × 4 cm), holding 3 mL of a solvent mixture (acetone, water, and 2-propanol in a ratio of 5:4:1) was fixed in the center of the integrating sphere chamber. A filter punch (30 × 8 mm) was immersed in the solvent mixture within the cuvette for optical detection. The wavelength-resolved absorbance (ABSISS(λ)) was acquired from 370 to 880 nm, defined as: 1ABSISSλ=-ln⁡IλI0λ, where I(λ) and I0(λ) denote the transmitted light intensities through the loaded and blank filters, respectively. Babs_uncoated(λ) is then converted as: 2Babs_uncoatedλ=100×ABSISS×ACF×F×T, where A is the total deposited area on the filter used by the high-volume sampler described in Sect. 2.2.1 (cm²); F is the flow rate of filter sampling (m³ min⁻¹); T is the duration of each filter sampling (min); and CF is the correction factor converting the ISS-measured absorption (multiple-angle absorption within the integrating sphere chamber) to the conventional one-way absorption (as measured by PAX). The method for determining the CF value has been described in our previous publication (Li et al., 2023b) and is represented in the Supplement (Sect.  S2).

A DRI Model 2015 Multi-Wavelength Thermal-Optical Carbon Analyser was used to split aerosol total carbon (TC) into organic carbon (OC) and elemental carbon (EC) employing temperature-regulated pyrolysis under controlled atmospheres. A 0.5024 cm² punch from a quartz filter was heated stepwise to 140 °C (OC1), 280 °C (OC2), 480 °C (OC3), and 580 °C (OC4) in a pure helium atmosphere and then combusted stepwise at 580 °C (EC1), 740 °C (EC2), and 840 °C (EC3) in a 2 % oxygen + 98 % helium atmosphere following the IMPROVE_A temperature protocol. The mass values of OC and EC were calculated as OC = OC1 + OC2 + OC3 + OC4 + OPC and EC = EC1 + EC2 + EC3 - OPC, where OPC represents pyrolyzed OC (Chow et al., 2007).

To acquire AAEs, filter transmittance and reflectance were continuously monitored using 7-wavelength diode lasers (405, 445, 532, 635, 780, 808, 980 nm), and the wavelength-specific light attenuation (ATN) was calculated accordingly. To mitigate filter matrix artefacts, including loading effects and multiple scattering (Chen et al., 2015; Chow et al., 2018; Peng et al., 2020), wavelength- and EC loading-dependent adjustment factors were applied to the raw ATN to obtain corrected ATNs (see Supporting Information Sect. S3, Table S2). Based on these, the AAEs for coated aerosols (AAE_coated) were calculated. The AAE_coated was then used to extrapolate Babs_coated(λ) from Babs_coated(870) in the following section.

A photoacoustic extinction spectrometer (PAX-870, Droplet Measurement Technologies) was deployed to monitor the in situ atmospheric Babs_coated(870) in real-time. Considering that we have only a PAX set with a single wavelength (870 nm), Babs_coated(λ) had to be extrapolated using the AAE_coated obtained in Sect. 2.3.1: 3Babs_coatedλ=Babs_coated870×λ870-AAEcoated It should be noted that extrapolating the single-wavelength measurement of PAX to other wavelengths is a source of uncertainty, which is specifically considered in Sect. 3.4. To minimize the potential bias caused by differences in filter substrates, the same batch of quartz filters were used for both thermal/optical analysis and integrating sphere measurements in this study.

The availability of Babs_coated(λ) from PAX and Babs_uncoated(λ) from ISS allows the acquisition of Babs,lensing(λ). As shown in Fig. 1, Babs,lensing(λ) is obtained by calculating the difference between Babs_coated(λ) and Babs_uncoated(λ), as: 4Babs,lensingλ=Babs_coatedλ-Babs_uncoatedλ Within this framework, the online PAX observations and offline filter-based ISS measurements share a common basis of daily-integrated aerosol populations (23.5 h d⁻¹, allowing 30 min for filter replacement) from the same sampling site and size range, rather than a strict match of instantaneous aerosol populations. The quality control procedures for the ISS-PAX system processing are detailed in Sect. S5 of the Supplement.

Although the two data streams are matched on the same daily sampling window, intraday variability is not resolved by this framework. AAE_coated is derived from a daily-integrated filter, whereas PAX measures Babs_coated(870) at high temporal resolution before being averaged over the corresponding 23.5 h period. If AAE_coated and Babs_coated(870) covary substantially within a day, applying a single daily AAE_coated to the daily-averaged PAX value may smooth this covariance and introduce bias into the reconstructed daily spectrum. Accordingly, the present results are interpreted at daily and longer (seasonal and annual) time scales rather than in terms of diurnal variability.

To decompose Babs_uncoated(λ), which is lensing free, into the individual contributions of BC and BrC, the DWIC algorithm was employed. Details of the DWIC algorithm have been described in our previous publications (Sun et al., 2017, 2021; Wang et al., 2021a) and in the Supplement (Sect. S4 and Fig. S1). Briefly, the iterative calculation uses two wavelengths (650 and 420 nm) and two reference materials: Carbon Black (CarB) as the proxy for BC, and Humic Acid Sodium Salt (HASS) as the proxy for BrC (Reisinger et al., 2008; Sun et al., 2017; Wang et al., 2021a; Wonaschütz et al., 2009). CarB was used as proxy for BC in diesel exhaust by Medalia et al. (1983) and HASS was used as proxy for BrC in wood combustion by Wonaschütz et al. (2009). In two previous studies conducted by our team, CarB and HASS were used as proxies for BC and BrC, respectively, from residential solid-fuel combustion (Sun et al., 2017, 2021). We carried over this philosophy to the current study. Calibration curves for CarB and HASS masses were established based on their respective absorption signals measured by the ISS at 650 (BC-dominated) and 420 nm (BrC-sensitive). Iterative optimization yielded the absorption coefficients of BC and BrC at these two wavelengths, i.e., Babs,BC(650), Babs,BC(420), Babs,BrC(650), and Babs,BrC(420).

The absorption coefficients of BC and BrC at wavelengths other than 420 and 650 nm (i.e., Babs,BC(λ), Babs,BrC(λ)) can be extrapolated from the values at these two wavelengths, constrained by their respective AAEs (AAE_BC and AAE_BrC). The AAE for BC or BrC is calculated as: 5AAEX=-ln⁡Babs,x650Babs,x420ln⁡650420

The absorption coefficient at any wavelength is then given by: 6Babs,xλ=Babs_uncoated420×λ420-AAEX where X refers to BC or BrC. The wavelength 420 nm in Eq. (6) can be replaced by 650 nm. Note that the selection of 420 and 650 nm was based mainly on the following considerations. The wavelength 420 nm lies in the short-wavelength region of visible light, where BrC has much higher light-absorption efficiency than at 650 nm; thus, it can serve as a BrC-sensitive wavelength. By contrast, 650 nm lies in the longer-wavelength visible region, where BrC absorption is much weaker than at 420 nm, whereas BC still maintains strong absorption. Therefore, 650 nm can be regarded as a BC-dominated wavelength. However, this does not exclude other wavelength pairs than the 650–420 pair only if they have sufficient spectral separation, different sensitivities to BC and BrC absorption, and stable light-intensity signals.

Every filter-collected sample was weighed to determine PM_2.5 concentration and analysed for aerosol carbon speciation (Fig. 2). Representative seasonal heterogeneity was observed in aerosol loadings and compositions.

As shown in Fig. 2, PM_2.5mass concentrations demonstrate pronounced seasonal variations, peaking in winter (107.03 ± 45.31 µg m⁻³) and reaching a minimum in summer (47.40 ± 12.30 µg m⁻³), consistent with regional emission patterns and meteorological conditions (Chen et al., 2017; Wu et al., 2016b). The seasonal trends in TC, OC, and EC concentrations generally mirrored those of PM_2.5, although the relative order of spring and autumn was occasionally reversed. For example, unlike PM_2.5 concentrations of spring > autumn, EC concentrations are of autumn > spring, implying differences in PM_2.5 composition arising from varied sources, transport, and ageing processes (Arhami et al., 2018; Ravindra et al., 2022; Song et al., 2022).

Thermal-optical carbon analysis provided distinct source signatures, as indicated by the char-EC/soot-EC ratios. Elevated ratios during high-combustion seasons like winter (1.81 ± 1.61) and autumn (1.50 ± 2.67) reflect predominant contributions from coal and biomass burning, as established by source apportionment studies (e.g., Han et al., 2010). In contrast, reduced ratios during spring (0.93 ± 0.77) and summer (0.39 ± 0.58) accord with vehicular-dominated emissions (Han et al., 2008; Liu et al., 2018a). Further speciation of OC to OC1, OC2, OC3, and OC4 suggests the influence of atmospheric processing. Low-volatility OC3–OC4 fractions constitute 40 %–54 % of total OC across all seasons, indicating the pathways of photochemical ageing and aqueous-phase processing that generate oxygenated semi-volatile compounds (Aswini et al., 2019; Li et al., 2018).

Having established the mass concentration and compositional context, we now examine the optical absorption properties of the coated aerosols. The daily light absorption of coated aerosol calculated in Sect. 2.3.2 was averaged seasonally and annually. Figure 3 shows the spectral dependence of Babs_coated(λ) across seasons and the annual average. Both the absorption intensity and AAE_coated exhibit a consistent seasonal order: winter > autumn > spring > summer. This order aligns with the seasonal trend in TC concentrations shown in Fig. 2. Since both BC and BrC are spectrally dependent components of TC, it is consistent that the AAE_coated values follow the same order as TC concentrations.

The AAE_coated values were highest in winter (1.300) and lowest in summer (0.892), with an annual mean of 1.053. AAEs lower than 1.0 are observed in spring and summer, seemingly challenging the traditional view that the AAE of carbonaceous aerosol should exceed 1.0, given that BC's AAE is typically 1.0 and BrC's AAE > 1.0 (Lack and Langridge, 2013). However, previous source-related experiments and Mie model calculations (Li et al., 2016; Liu et al., 2018b; Wang et al., 2021b) have reported a wide range of values for AAE_BC (e.g., 0.6–1.6) due to various confounding factors (e.g., aerosol size distributions, morphology, mixing state, or core-shell structure, etc.) (Curci et al., 2019; Guan et al., 2026; Helin et al., 2021; Liu et al., 2018b; Zhang et al., 2020a), implying the possibility of AAE values below 1.0 for coated aerosol. While referencing this broad range is instructive, the consistently low AAE_coated values in our spring and summer data may also be partially influenced by the net spectral effect of lensing enhancement and BrC blocking, which our subsequent deconvolution analyses aim to clarify.

To sum up this section (Sect. 3.1), the distinct seasonal characteristics of aerosol concentrations, carbon ratios, and AAEs reflect the diversity of the local ambient aerosol population, providing a suitable context for a comprehensive study of overall and decomposed light absorptions using the PAX-ISS hybrid method.

Using the daily wavelength-resolved absorption coefficients of BC, BrC, and apparent lensing effect (i.e., Babs,BC(λ), Babs,BrC(λ), and Babs,lensing(λ)) obtained via Eqs. (4) and (6), the daily, seasonal, and annual wavelength-resolved enhancement factors (Eabs(λ)) were calculated using Eq. (7).

Figure 5 shows the wavelength-resolved enhancement factors for the seasons and the year. A clear wavelength dependence is evident. Specifically, Eabs(λ) decreased monotonically toward shorter wavelengths in spring, summer, and autumn, while in winter it increased initially before declining in the short-wavelength range. That is, all seasonal and annual Eabs(λ) values turned downward as wavelengths approached the violet range. The observed decline in Eabs(λ) is mechanistically explained by the definition of Eabs (Eabs=1+Babs,lensing/Babs,BC) given the concurrent decrease in Babs,lensing (Fig. 5) and the increase in Babs,BC at shorter wavelengths (Fig. 4). This decline in Eabs at short wavelengths is likely associated with the strengthened blocking effect of BrC coatings, which reduces the net apparent lensing (Babs,lensing=Babs,Tlensing-Babs,blocking). The most extreme case occurred in summer at wavelengths below 465 nm, where observed Eabs(λ) values fell below 1.0, indicating that the net apparent lensing contributed negatively to BC light absorption. This is consistent with the finding of Luo et al. (2018) that Eabs(λ) can be below 1 in the ultraviolet region for BC with brown coatings due to blocking, which they termed the “sunglasses effect”. While the blocking effect of BrC has previously been examined mainly through numerical simulations (e.g., Luo et al., 2018; Zhang et al., 2021), our results provide suggestive field-based evidence consistent with this phenomenon rather than definitive proof of the underlying mechanism

Theoretical and experimental studies of lensing-induced absorption enhancement have yielded diverse results. Mie theory for spherical core-shell particles yields enhancement factors up to 3 (Bond et al., 2006; Jacobson, 2001; Schwarz et al., 2008). Such enhancement is supported by laboratory studies (Cappa et al., 2012; Schnaiter, 2005; Shiraiwa et al., 2010; Zhang et al., 2008) and is incorporated into climate models that work out total BC absorption (lensing included) either through simplified mixing-state assumptions (Chung, 2005; Penner et al., 1998) or by fixing the enhancement value at ∼ 1.5 (Flanner et al., 2007; Wang et al., 2014). In contrast, some field measurements have reported negligible absorption enhancement for ambient BC particles (Cappa et al., 2012, 2019; Fierce et al., 2016; Mbengue et al., 2021).

Complementing the wavelength-resolved results, we present the wavelength-averaged enhancement factor (Eabs, averaged over 370–880 nm) to assess the overall status of lensing. As shown in Fig. 6, the annual average Eabs was 1.69 ± 0.10. Seasonal averages varied from 1.09 ± 0.15 (summer) to 2.18 ± 0.08 (winter), with spring and autumn values of 1.81 ± 0.21 and 1.63 ± 0.06, respectively. Given the decisive role of lensing, the considerable seasonal divergence in Eabs is attributable to the varying contributions of Babs,lensing to Babs_coated (e.g., 4.6 % in summer versus 52.0 % in winter; see Fig. 4f). Other researchers have also reported diverse absorption enhancement factors in China, depending on specific conditions influencing lensing, particularly aerosol ageing statuses (Luo et al., 2018). For example, Cui et al. (2016) reported factors of 1.4 ± 0.3 for fresh combustion and ∼ 3 for aged BC at a rural North China Plain site. Chen et al. (2017) reported an average of 2.07 ± 0.72 for winter haze in northern China, with diurnal variation from 1.31 ± 0.29 (morning) to 2.23 ± 1.05 (afternoon) and 1.52 ± 0.75 (evening). Xu et al. (2016) even reported Eabs values of 2.6–4.0 for Beijing. Note that the definitions of Eabs vary a little in literature depending upon how to remove coatings or how to deal with BrC (a comprehensive comparison on different operational definitions is provided in Sect. S6 of the Supplement).

Beyond the comparison with literature values, a notable pattern emerges within our dataset: the seasonal Eabs values (Fig. 6) vary synchronously with PM_2.5 concentrations (Fig. 2); that is, higher PM_2.5 levels corresponded to higher absorption enhancement factors. This aligns with our previous findings that increased air pollution leads to greater absorption enhancement (Li et al., 2023b; Zhang et al., 2017, 2020b; Zhi et al., 2014). Increased air pollution in northern China usually results from stagnant weather that favors aerosol ageing, leading to the accumulation of primary emissions and the formation of secondary aerosols (Liu et al., 2024; Peng et al., 2021). The increased load of inorganic and organic pollutants enhances the likelihood and thickness of coatings on BC, thereby boosting the lensing effect (Li et al., 2023b).

This positive correlation is supported by the enhanced abundance of low-volatility, oxidised organic components (OC3–OC4, see Fig. 2) during the high-PM_2.5 seasons (winter and autumn). These components are markers of atmospheric ageing and secondary formation (Boonpeng et al., 2026; Chow et al., 2007; Tohidi et al., 2022), processes conducive to the development of thicker coatings on BC, thereby promoting a stronger lensing effect.

With sustained improvements in local air quality in China, conflicting climate influences may emerge: the warming effect could weaken due to a continued decline of Eabs, while the cooling effect from aerosol scattering could also weaken due to declining PM_2.5 concentration (Kelesidis et al., 2022; Samset et al., 2025; Xie et al., 2025). Future work should address this potential contradiction.