The field study was performed in the municipality of Loški Potok, Slovenia, in the rural village of Retje. The area is a small and shallow depression (area 1.5 km2, depth 150 m; 45°42′34.8′′ N, 14°34′53.8′′ E; Fig. 1). The basin-shaped topography of the site favors the formation of near-ground temperature inversions, especially in the coldest season, contributing to the accumulation of atmospheric aerosols emitted locally (Glojek et al., 2022). During temperature inversions, the denser and cooler air remains at the bottom of the depression, stopping mixing with warmer air at the top and inhibiting the vertical dilution of air pollutants.

The small village, with 690 inhabitants and 243 households, is encircled by a densely forested area; the local families use wood as the primary energy source for residential heating and cooking in the coldest season. The influence of aerosol traffic emissions is significantly low on the site, with an average of fewer than 100 vehicles circulating daily. The impact of industrial emissions is negligible, since the nearest atmospheric industrial emission sources are more than 10 km from the monitoring site (Glojek et al., 2020, 2022).

The local topography, the atmospheric stability, and the distinctive and predominant source of aerosol emissions make Retje a unique field laboratory to investigate the optical properties of organic aerosols and black carbon produced by residential wood burning under realistic conditions. The campaign was performed during wintertime from 1 December 2017 to 7 March 2018. We used a “twin monitoring scheme” with two fixed monitoring stations operating simultaneously (Fig. 1 and Table 1). One station was located at the bottom of the hollow in the middle of the village (main station, 715 m a.s.l.), while the second station was located at Tabor Hill (815 m a.s.l.) and served as a background station.

In both monitoring stations, the optical attenuation coefficient at seven wavelengths was continuously measured using filter-based absorption photometers (AE33 Aethalometer, 370 to 950 nm, Aerosol Magee Scientific). The AE33 instruments used filter tapes, model M8060, made of PET polymerized polyester (59 %) and fiberglass (41 %). The particle number concentration (N) and particle number size distributions (PNSDs) were monitored at Retje (10–800 nm) and Tabor Hill (10–600 nm) using mobility particle size spectrometers (MPSSs). At the village, a reference MPSS (TROPOS ref. no. 1, high-voltage supply of positive polarity) set up with a bipolar diffusion charger (radioactive source: 85Kr), a differential mobility analyzer (DMA, Hauke-type medium), and a butanol-type condensation particle counter (CPC, TSI model 3772) operated, whereas, at the background station, a TSI MPSS (high-voltage supply of negative polarity) set up with a bipolar diffusion charger (radioactive source: X-ray), a DMA (TSI 3081), and a water-type CPC (TSI model 3785) was installed. A multiple-charge inversion routine was applied to the raw mobility distributions to calculate the final PNSD (Pfeifer et al., 2014); additional corrections were applied to the PNSD, including CPC counting efficiency and particle losses due to diffusion in the inlet and sampling tubes and internal particle diffusion (corrected via the “equivalent pipe length” method; Wiedensohler et al., 2012).

Filter samples of particulate matter (PM10) were collected every 12 h at the village station (06:00 to 18:00 and 18:00 to 06:00 local time) using a high-volume sampler (DHA-80, Digitel). PM10 mass concentrations were determined gravimetrically in the laboratory following the European Union standard EN 12341. The quartz fiber filters (150 mm diameter) were preheated before sampling for at least 24 h at 105 °C to minimize blank values and frozen after sampling until their characterization in the laboratory; the weighing was done using a microbalance (AT261 Delta Range, Mettler Toledo). The PM10 filters were analyzed to estimate the particle's chemical composition, including organic and elemental carbon (OC / EC), ions (NH4+, Cl-, Na+, K+, Mg2+, Ca2+, NO3-, SO42-, and C2O42-), and levoglucosan. Mass concentrations of OC / EC were quantified following the EUSAAR-2 Protocol (Cavalli et al., 2010); ions were determined using ion chromatography (Dionex ICS-3000) of ultrapure water extracts (further details in Fomba et al., 2014); levoglucosan was quantified using high-performance anion exchange chromatography coupled with an electrochemical detector (HPAEC-PAD; Iinuma et al., 2009).

The total carbon (TC) mass concentration at the village station was measured using an online total carbon analyzer (TCA08, Aerosol Magee Scientific; Rigler et al., 2020). The dual-chamber instrument uses an online thermal method to quantify the total carbonaceous fraction in atmospheric aerosols. In one chamber, the sample is collected over a quartz fiber filter (47 mm diameter) and heated to 940 °C, transforming the carbon compounds into CO2. The amount of CO2 is measured before and after combustion by a CO2 detector and is later integrated to calculate the total carbon mass concentration. Simultaneously, the second chamber collects a new aerosol sample (sampling time adjustable from 20 min to 24 h). Both chambers alternate between sampling and analysis, enabling online functionality. Further details about the MPSS, DHA-80, and TCA08 operating principles are given in the Supplement.

Cyclones with a PM2.5 cutoff were used to sample aerosols for the AE33s, MPSSs, and TCA08; Nafion^® Perma Pure air dryers (length = 1.5 m) kept the relative humidity of the AE33 and MPSS samples below 40 %. The instruments operated at ambient room temperature. The DHA-80 high-volume sampler was equipped with a PM10 impactor-type inlet. Table 1 shows the specifications and operating conditions of the instruments used during the campaign.

The quality of the instrument measurements was assured by intercomparison, calibration, and maintenance in the laboratory. The TROPOS ref. no. 1 MPSS and the TSI MPSS were calibrated and intercompared against a reference MPSS (TROPOS reference no. 4 MPSS, set up with a CPC TSI model 3772) and a reference CPC (TSI CPC, model 3010) at the World Calibration Centre for Aerosol Physics (WCCAP) in Germany. The comparison against the reference MPSS and CPC showed acceptable deviations within the range of ±10 % for the mean particle size distributions and the integrated number of particle concentrations. Further detailed results from the intercomparisons are shown in Glojek et al. (2020, 2022). The AE33 and the TCA08 were maintained as the manufacturer indicated (Aerosol Magee Scientific, 2018, 2022), including the inspection of the inlet flow and sampling lines, flow calibration, and leakage tests.

The PM1 mass concentration was defined as the sum of BC, OA, and inorganic aerosol (InA) masses, similarly to Setyan et al. (2012). Accordingly, the hourly OA mass concentration was calculated using a mass balance as follows: 2[OA]=[PM1]MPSS-[eBC]AE33-[InA]PM. For the previous calculation, we considered the good agreement between the PM10 mass concentrations from the filters and the 12 h averages of PM1 from the MPSS (see Fig. 2; orthogonal fit: slope = 0.9, R2=0.96). The comparison of PM1–PM10 suggests that most PM10 is composed of PM1 (∼ 90 %). This approach, however, could be an important source of uncertainty in determining the hourly OA mass concentration, since a fraction of OA might fall in the 1–2.5 µm size range; in contrast, the fraction of BC is most probably below the PM1 fraction (Sect. 3.3 shows an analysis of uncertainty).

The hourly PM1 mass concentration was estimated from the MPSS volume size distribution, with the following assumptions: (i) the bulk aerosol density is constant (ρ=1.4 g cm-3, a typical value attributed to aerosols with relatively large fractions of organic species; Rissler et al., 2014; Turpin and Lim, 2001) and (ii) the aerosol particles have spherical shape (the mobility diameter is equivalent to the volume-equivalent diameter). Please note that all the size distributions from the MPSS in Retje (mobility diameters from 10 to ∼ 800 nm) were used in the PM1 mass calculation to cover the aerodynamic diameter of PM1. Mass concentrations of PM1 were not calculated for the background station, considering the maximum mobility diameter reached by the TSI MPSS.

The BC mass concentration was estimated from the optical measurement of absorption from the AE33 Aethalometer, denoted consequently as equivalent black carbon (eBC) (Petzold et al., 2013). The local mass absorption cross-section for BC (MACBC) was determined as the slope from the orthogonal fit between the 12 h averaged aerosol light absorption at 950 nm from the AE33 babs(λ) and the EC mass concentration derived from the thermo-optical analysis of the PM10 filters (see Sect. 3.2.3). Despite the differences between BC and EC given by their operational definitions (Bond and Bergstrom, 2006; Petzold et al., 2013), we assume, for this study, that both species are comparable and that at 950 nm BC dominates the light absorption (Zanatta et al., 2016). Accordingly, the eBC mass was calculated as follows: 3eBC=babs950nmHarm.MACBC950nm. The mass fraction of InA in PM10 (Cl-, NH4+, NO3-, SO42-, C2O42-, Na, K, Mg, and Ca) was, on average, 15 % of the total PM mass. For PM1, we assumed a similar percentage contribution of InA, considering the correlation between PM10 and PM1 (see Fig. 2) and a homogeneous distribution of the inorganic aerosols in the PM mass. The uncertainty of the slope in Fig. 2 was estimated using error propagation as outlined in Sect. 3.3. This estimation accounted for the individual contributions of the errors involved in both the PM1 calculation and the gravimetric determination of PM10. The final uncertainty was determined to be 15 %.

The estimated hourly OA mass concentration (OAMPSS, Eq. 2) was compared to the OC mass from the total carbon analyzer (OCTCA; see Eq. S4) and the OC from filters (OCfilters). In both cases, a good agreement was observed between OA and OC (Fig. S1 in the Supplement, OAMPSS vs. OCTCA: R2=0.95, OAMPSS vs. OCfilters: R2=0.97), suggesting that OAMPSS is a good approximation in the study site. The slopes in both comparisons (OAMPSS vs. OCTCA: 2.0, OAMPSS vs. OCfilters: 1.6) represent the local OA / OC ratio. The estimated OA / OC ratios differ due to the distinct analytical procedures from both methods and sampling periods (1 h averaged data from TCA08 and 12 h data from filters) (Brown et al., 2013). Nevertheless, both OA / OC ratios fall within the range of ratios reported in the literature (Srinivas and Sarin, 2014b; Xing et al., 2013).

Please note that in the following, OAMPSS is referred to as OA.

To estimate the climate impact of the RWB aerosol particles emitted in Retje, we used the simple forcing efficiency (SFE), which quantifies the perturbation caused by the emitted aerosol particles on the radiative balance of the Earth's atmosphere (Chen and Bond, 2010; Choudhary et al., 2021). For this purpose, the equation proposed by Chen and Bond (2010) was used: 4dSFEdλ=-14dS(λ)dλτatm2(1-Fc)21-as2×β(λ)×MSC(λ)-4as×MAC(λ), where SFE is given in W g-1; dS(λ)dλ is the solar irradiance (W m-2 nm-1) obtained from the reference solar spectra from ASTM G173-03; and τatm and as are the atmospheric transmission (0.79) and the surface albedo (Earth average 0.19, fresh snow 0.80), respectively, whose values were taken from the study of Chen and Bond (2010). Fc is the cloud fraction (assumed to be 0.6); β(λ) is the light backscatter fraction; and MAC(λ) and MSC(λ) are the mass absorption and mass scattering cross-sections (m2 g-1), respectively. β(λ) was estimated by the mathematical relation with the asymmetry parameter g(λ) proposed by Sagan and Pollack (1967): 5β(λ)=121-g(λ).

The different categories of atmospheric stability in Loški Potok were identified according to the potential temperature gradient (∂θ∂z), expressed in K m-1 and calculated as the difference in the absolute potential temperature (θ) from both sites (Eq. 7): Tabor Hill at the top of the valley (θbackground) and the village of Retje at the bottom (θvillage). Using the potential temperature is advantageous, since it discounts the compressibility effect caused by the air pressure. θ is the temperature a parcel of air would have if it expanded or were compressed adiabatically (no heat is added or subtracted) and were brought to a reference pressure (Hartmann, 2016). Hourly values of θ for Retje and Tabor were calculated as shown in Eq. (8), using the measurements from the meteorological sensors operating during the campaign (Table 1). 7∂θ∂z=θbackground-θvillage/dz,

8θ=T×P0PR/Cp, where T is the absolute temperature, P0 is the reference pressure (standard atmospheric pressure, 1 atm), P is the local pressure, R is the gas constant for air, and Cp is the specific heat capacity of air at constant pressure (R/Cp=0.286 for ambient air; Wallace and Hobbs, 2006).

The categories of atmospheric stability are given according to ∂θ∂z: when ∂θ∂z>0, the potential temperature increases with height, the atmosphere is stable, and near-ground temperature inversions occur; when ∂θ∂z=0, the potential temperature is uniform, there are no net upward or downward buoyancy forces, and the atmosphere is neutral; when ∂θ∂z<0, there is a decrease in the potential temperature, the atmosphere is unstable, and vertical motions within an air parcel are favored (Hartmann, 2016). During the unstable conditions at Loški Potok, ∂θ∂z ranged from -5 to 0 K m-1, while for stable conditions ∂θ∂z ranged from 0 to 12 K m-1. The wide range of positive ∂θ∂z values motivated us to partition the inversion periods into two subcategories: weak inversion and strong inversion. The final categories of atmospheric stability used in the analysis are given in Table 2.

Deming's total least-squares regression was used to compare measurements from different methods or instruments, estimate the mass absorption cross-sections (MACs), and evaluate correlations among variables (R package “deming”; Therneau, 2018). Deming regression fits a couple of variables considering the independent measurement errors of both X and Y. The errors are assumed to be normally distributed, and the error ratio (Eratio) is constant (Deming, 1964). For Eratio=1, the regression results are equivalent to the orthogonal regression. Measurement data and calculations were processed in the software R version 4.0.0 (R Core Team, 2020).

Extremely high values for aerosol mass and particle number concentrations and light absorption coefficients were measured in Retje, Loški Potok, under conditions of near-ground temperature inversion. Figure 3 shows the time series of the OA and BC mass concentrations (Fig. 3a and b), the total light absorption coefficient at 370 nm (Fig. 3c), and the particle number size distribution (Fig. 3f) from the campaign period. For conditions of strong inversion, the OA and BC concentrations ranged from 1.9 to 270 and 0.1 to 24 µgm-3, respectively. In contrast, when the atmosphere was unstable, the OA and BC fluctuated from 0.17 to 120 and 0.0 to 8.1 µgm-3. The mean total light absorption coefficient at 370 nm was 260 Mm-1 (max 1100 Mm-1) under strong inversion, while the mean value registered under an unstable atmosphere was 56 Mm-1 (max 330 Mm-1). The mean total particle number concentration (10–600 nm) was 17×103 particles cm-3 under strong inversion, compared with the mean concentration of 6.1×103 particles cm-3 for unstable atmosphere (see Table 3).

Table 4 shows the statistical summary for the PM10, EC, OC, and levoglucosan mass concentrations. For these, the 12 h predominant atmospheric stability was also identified for periods from 06:00 to 18:00 and from 18:00 to 06:00 LT. During periods when strong inversions prevailed, the mass concentrations of PM10, OC, and EC were the highest, reaching mean values of 110 µgm-3 (max 200 µgm-3), 47 µgm-3 (max 94 µgm-3), and 6.4 µgm-3 (max 15 µgm-3), respectively. The wood-burning tracer levoglucosan also exhibited higher concentrations during predominant temperature inversion periods, reaching a mean concentration of 6.7 µgm-3 (max 17 µgm-3).

The 1 and 12 h measurements showed decreased values during weak-inversion, neutral, and unstable atmosphere periods. Tables 3 and 4 show the statistical summaries of the aerosol measurements by categories of atmospheric stability and for the entire campaign period.

Episodes of strong temperature inversion are of primary interest in this study, since they favor the accumulation of aerosol particles produced by a predominant source: RWB. Presumably, the concentrations measured in the village at the bottom of the hollow are less impacted by external aerosol sources under temperature inversion. Therefore, its characterization gives an authentic fingerprint of residential-wood-burning emissions in a real environment. Strong and weak temperature inversion appeared 28 % and 31 % of the time based on hourly measurements, respectively. The more extended episodes of prevailing thermal inversion occurred from 3 to 7 December 2017, 17 to 26 December 2017, 29 December 2017 to 1 January 2018, and 14 to 17 February 2018.

The effect of atmospheric stability on the accumulation of aerosol particles in the hollow is observed when comparing the village and the background measurements. Figures 4 and 5 show the differences (Δ) in the particle number (N) and aerosol mass concentrations by atmospheric stability. Please note that deltas in the number concentration were calculated using ∼ 600 nm as the upper limit of both size distributions (main and background stations) for comparability. The values of ΔN were, in general, positive and largest under strong inversion, while the lowest and closer-to-zero values were observed for unstable atmosphere. From Fig. 4, the significant contribution of RWB emissions for particles in the size range of 50 to 150 nm is evident, with a median ΔN50-150=47×102, 22×102, and 15×102 particles cm-3 under strong inversion, weak inversion, and unstable atmosphere, respectively. In contrast, the median ΔN10-50 values were 12×102, 9.8×102, and 9.6×102 particles cm-3, and medians for ΔN150-600 values were 24×102, 9.4×102, and 5.3×102 particles cm-3, for each category of atmospheric stability, respectively. In general, ΔN10-50 exhibited the lowest change among the stability conditions, given that from strong inversion to weak inversion, ΔN50-100 reduced by 50 % and ΔN100-600 by 60 %. We hypothesize that the almost constant ΔN10-50 is explained by the predominant sources of ultrafine particles: secondary aerosol particles, sea salt, and traffic emissions (Leoni et al., 2018). All these three sources might have an impact on the local and background concentrations at the study site. ΔBC showed similar trends to ΔN. For strong inversion, weak inversion, and unstable atmosphere, the mean ΔBC was 4.4, 1.5, and 0.9 µgm-3, respectively. In some cases, the values of ΔBC were negative, meaning the concentrations in the background were higher than in the village.

Error propagation was used to estimate the uncertainty in the RWB MACOA, considering the contribution of the OA mass concentrations and the BrC light absorption coefficients. The mathematical expression representing the fit between both variables has the form y=m⋅x, where y is babs,BrC(λ), x is OA, and m is MACOA. Rearranging the equation, MACOA=f=y/x. For uncorrelated variables, the propagated error of the function (σf) can be calculated using the following quadratic sum: 13σf=δfδxσx2+δfδyσy2, where σx and σy are the absolute errors of x and y.

To estimate the MACOA uncertainty, the propagated errors of babs,BrC(λ) and OA were first calculated individually. Based on the OA mass balance (Eq. 2), the uncertainty in the OA mass concentration includes the contribution of the following individual components: (i) PM1 mass concentrations estimated from the MPSS, (ii) the eBC mass concentrations derived from the AE33, and (iii) the mass concentration of inorganic species in the PM10 filters. The PM1 uncertainty was assumed to be 17 % based on the calculations of Buonanno et al. (2009) and the MPSS intercomparison in the laboratory. This estimation accounts for contributions from the sampling flow rate, the volumetric diameter, the diffusion efficiency corrections, and the particle density. The uncertainty in the eBC mass concentration is assumed to be 5 %, corresponding to the EC uncertainty, as eBC was normalized to EC using the local MACBC. The uncertainty in EC corresponds to the reproducibility of the thermo-optical analysis following the EUSAAR protocol. The uncertainty contribution of the insoluble inorganics was 20 %, considering the deviation resulting from assuming the InA fraction in PM10 to be the same as that in PM1. Additionally, we considered a reproducibility error based on Leiva et al. (2012).

In the uncertainty calculation for babs,BrC(λ), the following contributions were considered: (i) the AE33 light absorption coefficients, (ii) the harmonization factor H, and (iii) the BC absorption Ångström exponent. The uncertainty in the AE33 total light absorption coefficients is assumed to be 25 % and mainly proceeds from the variabilities in the unit-to-unit intercomparison and the multiple-light-scattering correction factor C (Cuesta-Mosquera et al., 2021; Müller et al., 2011; WMO, 2016). Given the presence of correlated variables in the mathematical definition of babs,BrC(λ), the uncertainty calculation included the covariance when dealing with total light absorption coefficients at different wavelengths measured by the AE33. The propagated uncertainty in H was calculated based on the simultaneous AE33–MAAP field measurements in Melpitz, Germany, during wintertime (2018/19). For this, the uncertainty in the MAAP light absorption coefficients of 12 % was included (Petzold and Schönlinner, 2004). The calculated uncertainty in winter H for Melpitz (median = 1.9) is 23 % and is assumed constant for the study in Loški Potok. The uncertainty in the BC absorption Ångström exponent was assumed to be 10 %, coming from the deviation of the AAEBC values ranging between 0.8 and 1.2 (Lack and Langridge, 2013). Although the assumption of AAEBC = 1 might add significant error to the apportionment of the light absorption coefficients (BC / BrC) and aerosol optical properties, the value was used as a fair estimate based on the community standards. The values of uncertainty estimated for babs,BrC(λ) were 48 % (370 nm), 26 % (470 nm), 19 % (520 nm), 14 % (590 nm), 11 % (660 nm), and 6 % (880 nm).

The final propagated uncertainty for the MACOA,370nm was 46 %, with a major dependency on the apportioned OA light absorption coefficient. The uncertainty in MACOA increased with the wavelength due to lower MACOA values and light absorption coefficients attributed to BrC; for instance, the uncertainty in MACOA,470nm was 60 % and > 70 % for MACOA,520nm. Similarly, the uncertainty in the PM1/ PM10 ratio (slope in Fig. 2) was calculated through error propagation. Besides the contribution of PM1, the error for PM10 was considered and assumed to be 10 %, accounting for sampling errors (air volume) and reproducibility (Hafkenscheid, 2013; Leiva et al., 2012). The final determined uncertainty for the slope PM1/ PM10 was 15 %.

The model described in Sect. 2.4 was used as a sensitivity analysis tool to assess the climate impact of the light-absorbing properties of the RWB aerosol particles at Loški Potok. Figure 9 shows the spectral variation in the SFE for two different types of surfaces: fresh snow (as=0.80) and Earth average (as=0.19). In each case, the forcing efficiency was calculated for two scenarios: (i) assuming OA to be light-absorbing species (imaginary refractive index kBrC from the literature) and (ii) assuming OA to be non-absorbing (imaginary refractive index kBrC=0). The SFE was calculated for six of the seven wavelengths covered by the AE33. The total radiative forcing (RF) was calculated by integrating the area under the curves using the trapezoidal rule (blue and yellow lines in Fig. 9).

The resulting SFE was larger and positive for bright snow and relatively small for the Earth-average surface. For non-absorbing OA, the SFE was lower than for absorbing OA with slightly negative values for the Earth-average surface. The comparison among surfaces indicates that RWB aerosols have a more significant impact over bright surfaces, for instance, the Arctic or areas covered by snow, typical during the coldest season when the most significant emissions of OA are expected due to more intense RWB. We also observed that SFE is larger at 470 nm despite the significantly higher mass absorption cross-section calculated at 370 nm. This observation is attributed to the larger solar irradiance dS(λ)/d(λ) reported in the blue region (1.1 to 1.4 W m-2 nm-1) compared to the values from the near UV (0.0 to 0.8 W m-2 nm-1).

For fresh snow, the corresponding RF of the RWB aerosols was 61 and 44 W g-1 for absorbing OA and non-absorbing OA, respectively. For an Earth-average surface, the RF was 0.2 and -3.9 W g-1 for absorbing and non-absorbing OA. The RF was 2 times higher for a snow-like area and passed from cooling to warming for an Earth-average surface by taking OA as light-absorbing species. Our calculations show the crucial influence of the OA in atmospheric warming via the lensing effect of coated BC and BrC absorption in shorter wavelengths; nevertheless, robust climate models are essential to reporting definite radiative forcing figures, since these consider further atmospheric processes and aerosol properties such as aerosol–cloud interactions, aerosol hygroscopicity, and the total vertical column of aerosols.