Two distinct measurement locations were selected for this study. The first one is located in the urban area of Ljubljana (LJ, capital city of Slovenia), which lies in the central part of Slovenia (Europe) (Fig. 1). The second measurement location was in a small town, Ajdovščina (AJ), located in the Vipava valley in the western part of Slovenia. Measurement campaigns lasted from autumn 2016 to spring 2017 (23 November 2016 to 20 May 2017) in Vipava valley and from winter 2017 to summer 2017 (1 February 2017 to 8 June 2017) in Ljubljana. Due to its basin location, Ljubljana is characterized by poor ventilation and frequent occurrence of persistent temperature inversions (Kikaj et al., 2019), which constrains pollutants emitted from surface sources within the limited air volume inside the basin. During stable atmospheric conditions, especially in the SNBL, a thin layer of drainage winds (colder air, adjacent to the ground, flowing downhill under the influence of gravity) and a flow of air from the edge of the city towards the centre (formed due to the heat island) governs air circulation within the Ljubljana basin (Stull, 1988; Ogrin et al., 2016). Ljubljana is characterized by temperate continental climate, with a significant seasonal temperature cycle.

The population of the wider Ljubljana basin is around 500 000, of which 287 000 live in the urban municipality of Ljubljana. Many more than 100 000 daily commuters from other municipalities represent additional traffic flow on working days (Ogrin et al., 2016). Besides traffic-related air pollution, emissions from combustion of biomass fuel for residential heating are a significant source of particulate concentrations in the whole country (Gjerek et al., 2018), not only in rural areas, but in Ljubljana as well. Although district heating is provided in several areas of the city, the use of wood boilers and fireplaces is a common practice.

The population of the second area of interest including surrounding villages is relatively small, with about 7000 residents living in the town of Ajdovščina. The Vipava valley is confined to the north by the steep ridge, which rises up to about 1000 m a.s.l., and to the south by the Karst plateau with an average altitude of about 300 m. Due to the complex topography, the valley usually experiences two extreme cases of atmospheric stability conditions. On the one side, stable atmospheric conditions can last for several days, leading to the formation of strong vertical aerosol gradients, which are followed by frequent occurrences of strong downslope bora wind (Mole et al., 2017; Wang et al., 2019). A highway connecting the central part of Slovenia with Italy runs through the valley on the southern border of the town, around 800 m away from our measurement site. The Mediterranean climate of this area is responsible for mild winters and warm summers, with residential heating mainly limited to the cold season, from November to February, with biomass fuel being the primary source of energy.

From a geological point of view, the city of Ljubljana lies in the neotectonic basin with extensive and thick accumulations of Quaternary glaciofluvial sediments on the northern and central parts (gravel and conglomerate), whereas the southwestern part of the Ljubljana basin is filled with lacustrine and paludal sediments (Janža et al., 2017). The maximum thickness of sediments is around 170 m. Non-consolidated Quaternary sediments are permeable enough to allow spatially and temporally homogeneous Rn exhalation rate.

The geological structure of the broader area of Vipava valley results from Tertiary thrust of Cretaceous limestone, which forms the steep northeastern ridge of the valley, on the Eocene flysch rocks, forming the valley floor. Flysch rocks consist of alternating layers of marlstone and carbonatic sandstone. Due to physical weathering of the limestone, a large amount of limestone scree material has been formed and deposited on the underlying flysch rocks on the slopes of the northeastern ridge. The valley floor is covered by clayey weathered residual of flysch rocks with fine flysch scree (Jež, 2007). Spatially homogeneous Rn exhalation rates can be expected along the valley.

Measurements of black carbon concentration were conducted at two sites at each location, Ljubljana and Vipava valley, one at the urban background and the other one at the higher altitude (Fig. 1), in order to provide insight into the extent of the vertical aerosol mixing. Periods during which similar BC concentrations were measured at both sites indicate time periods when MLH reached or exceeded altitude differences between both sites. Although this kind of measurement composition certainly indicates periods of stable PBL conditions, detection of the exact time of MLH reaching the upper site is more uncertain due to diffusion mixing (in the case of Ljubljana) or local slope winds (Leukauf et al., 2016) (Vipava valley), and therefore it does not provide undisturbed MLH evolution characteristics for the whole valley/basin.

The urban background site of the Slovenian Environment Agency (ARSO) was used for BC measurements in the city of Ljubljana (295 m a.s.l.), while measurements at the Golovec Astronomical and Geophysical Observatory (GOL), 100 m above Ljubljana (395 m a.s.l.), were used as the hill site. The inlet at ARSO was about 4 m above the ground, while the inlet at GOL was about 2.5 m above ground. Measurements in the Vipava valley were conducted about 12 m above ground level (120 m a.s.l) on the roof of the building of the University of Nova Gorica, located in the town of Ajdovščina (AJ). About 830 m higher (950 m a.s.l.), on the northeastern ridge of the valley, the second measurement site was installed at the Otlica meteorological observatory (OT) of the same university.

Aerosol light absorption and corresponding mass equivalent black carbon concentration (BC) were measured at seven different wavelengths (370–950 nm) using the Aethalometer model AE33 (Magee Scientific, Aerosol d.o.o.), with the “dual spot” technique used for real-time loading effect compensation (Drinovec et al., 2015). Flow rate was set to 5 L/min and the measurement time resolution to 1 min. A TFE-coated glass fibre filter was used with the multiple-scattering parameter (C) set to 1.57. The mass absorption cross section σair of 7.77 m2 g-1 was used to convert the optical measurement at 880 nm to BC mass concentration.

Aethalometer measurements at different wavelengths provide an insight into the chemical composition of light-absorbing particles. The so-called Aethalometer model (Sandradewi et al., 2008a) was used to apportion BC to traffic (BCTR) and biomass burning (BCBB) sources. The model uses an a priori assumed pair of absorption Ångström exponents (AAEs) for traffic (AAETR) and biomass burning (AAEBB) to determine the contribution of both sources. AAETR and AAEBB were set to 1.0 and 2.0, respectively. Further discussion on the choice of AAE pair used for source apportionment is provided in Sect. S1 of the Supplement.

Radon measurements were conducted at both measurement locations, in the city of Ljubljana on the floor of the basin and on the floor of Vipava valley, close to the town of Ajdovščina. Measurements cover longer periods than BC measurements: from 11 November 2016 to 31 May 2017 in Vipava valley (with about a 1-month gap in March 2017 due to instrument malfunction) and from 14 December 2016 to 8 June 2017 in Ljubljana. At both measurement sites, instruments were installed outdoors under the roof of a single-family house (to shelter instruments from environmental effects, but otherwise open), surrounded by unperturbed natural soil ground. Both sites were selected in the area that is subjected to the same boundary layer characteristics as aerosol measurements. Instruments were installed 1 and 3 m above ground in Ljubljana and Vipava valley, respectively. Radon activity concentration (CRn) was measured using an AlphaGUARD PQ2000 PRO (Bertin Instruments) radon monitor. In the instrument, the measured gas diffuses through a large-surface glass fibre filter into the ionization chamber. The instrumental lower limit of detection is 2–3 Bq m-3 at 1 h time resolution. In order to decrease noise, radon measurements were smoothed by applying a FFT filter with a cut-off frequency of 0.25 h-1. Comparison of smoothed and raw Rn measurements is shown in Fig. S6. Due to sampling in diffusion mode, 1 h time lag was considered when combining CRn data with other measurements.

Meteorological parameters, such as air temperature (T), wind speed and direction (ws, wd), amount of precipitation, and snow cover were provided by the Slovenian Environment Agency (ARSO) for the Ljubljana measuring location. In the Vipava valley, all meteorological parameters are measured at the meteorological station situated at the valley floor close to the town of Ajdovščina, whereas wind data were collected at the rooftop of the University of Nova Gorica building in Ajdovščina as a part of research conducted at the Centre for Atmospheric Research (Mole et al., 2017).

The MLH dataset, obtained from the NOAA Air Resources Laboratory (NOAA-ARL) Global Data Assimilation System (GDAS) database (Rolph et al., 2017), was considered as supplementary information for comparison with the effective MLH values derived from the box model. The archived dataset has a spatial resolution of 1∘ and temporal resolution of 3 h. Although spatial resolution is not fine enough to capture local micrometeorological characteristics, it gives an estimation on the wider area PBL stability and effective mixing height.

Traffic count data for Ljubljana were provided by the municipality of Ljubljana for the whole period of measurements for several different locations within the city.

Two complementary methods were used for detection of MLH and comparison with MLH derived by the box model. Scanning mobile Mie-scattering lidar is used at the University of Nova Gorica for studies of bora wind (Mole et al., 2017), aerosol properties and PBL characteristics (Wang et al., 2019) in the Vipava valley. Detailed lidar configuration and performance are provided by He et al. (2010). In our study, MLH was estimated based on the retrieval of range-corrected lidar signal in selected periods. On the other hand, vertical BC concentration profiles were measured over the Ljubljana basin by ultralight aircraft on selected days from February to May 2017. A lighter modified version of the Aethalometer AE33 with an isokinetic sampling inlet was used for BC vertical profile measurements. Measurements provided useful information about aerosol vertical dispersion characteristics and MLH estimation (Ferrero et al., 2011). Further details about the analysis approach are provided in the Supplement (Sect. S2).

The box model approach introduced in previous studies (Sesana et al., 2003; Griffiths et al., 2013; Salzano et al., 2016; Williams et al., 2016; Vecchi et al., 2018) employs the Eulerian approach, including a constant radon source (ERn) and vertical entrainment of air masses from the residual layer. Salzano et al. (2016) improved the model performance by considering the variability in the soil radon exhalation rate, where the authors showed up to a 10 % difference in modelled MLH compared to the model using a constant Rn source. In this paper we applied the approach introduced by Williams et al. (2016), where an inclusion of a simplified horizontal advection term allows the quantification of local emissions of air pollutants.

Considering a vertically well-mixed box (box dimension discussed in detail in Sect. 2.6.1) with species concentration Cs, the mass of species “s” in a column of air within the effective MLH (h) over 1 m2 at time ti depends mainly on the emissions (Es) from the surface and the remaining mass of species from the previous time period (ti-1). When ML is growing (cs+), there is an additional encroachment of species, which remained in the residual layer from the previous day, while in the case when this layer is shrinking (cs-), a part of mass is considered to be removed from the mixing layer (Eq. 1). 1Csihi=EsΔTs+Csi-1hi-1e-λs′dt+csi-1±(hi-hi-1)e-λs′dt The term ΔTs (Eq. 2) includes correction due to decay of species in time period dt=ti-ti-1 , which is characterized by decay constant λs′. If decay rate is very slow, decay of species within dt becomes negligible; thus ΔTs→dt. 2ΔTs=1-e-λs′dtλs′ Decay constant λs′h-1 takes into account temporal decay and horizontal advection. The temporal decay constant λs (h-1) accounts for internal sinks due to chemical reactions, dry and wet deposition, or radioactive decay. Horizontal advection assumes exponential decrease in species concentration downstream (Eq. 3) and is characterized by spatial decay constant γs (m-1): 3λs′=λs+Uγs, where U represents layer-averaged wind speed. A small uncertainty is introduced to the model, since wind data were available only from standard meteorological measurements at the height of 2 m above the surface.

Three different cases can be parameterized during the course of a day.

During stable conditions, when hi=hi-1, Eq. (1) is reduced to Eq. (4): 4Csi-Csi-1e-λs′dt=EΔTshi. After the sunrise when PBL starts to grow (hi>hi-1), a volume of air mass from the residual layer is incorporated into the expanding ML and the term cs± from the last part of Eq. (1) is modelled as cs+ (Eq. 5): 5csi-1+=cs0e-λs′ti-1-t0, where cs0 is species concentration from the previous day at time t0, just before the afternoon transition to SNBL. cs+ represents the concentration of species in the residual layer.

When PBL is shrinking (hi<hi-1) a volume of air is decoupled from ML and forms the residual layer. cs± of Eq. (1) is set to csi-1-=Csi-1.

The first phase of modelling is focused to the quantification of the effective MLH based on atmospheric Rn concentration measurements. Rn data with 1 h time resolution were first smoothed by applying the FFT filter with a cut-off frequency of 0.25 h-1 in order to decrease noise level, since small changes of Rn concentration can cause unexpected fluctuation in the calculated MLH. Assuming a constant, spatially homogeneous radon source, which extends beyond the limits of our modelled area, the spatial decay constant in Eq. 3 can be approximated to zero (γRn=0) and decay constant λRn′ is equal to the radon radioactive decay constant: λRn=0.0076h-1. Radioactive decay accounts for less than 1 % of CRn decrease during the course of 1 h.

For stable atmospheric conditions, when hi=hi-1, Eq. (4) is simplified to 6hi=ERnΔTRndCRn, where dCRn represents the difference in radon concentration measured in the time period dt: 7dCRn=CRni-CRni-1e-λRndt. The condition of expanding or shrinking ML is tested by comparing the difference of concentration with emission of Rn to the ML with MLH=hi-1 in the same time period. In the case of expanding ML, change of Rn concentration is smaller than expected for stable MLH: dCRn<ERnΔTRn/hi-1 (Eq. 8), whereas in the case of shrinking ML, concentration increases faster than would be expected for stable MLH: dCRn>ERnΔTRn/hi-1 (Eq. 9). Effective MLH is then calculated for the two separate conditions as 8hi=ERnΔTRn+hi-1CRni-1-CRni-1+e-λRndtCRni-CRni-1+e-λRndt, 9hi=EΔTRnCRni-CRni-1e-λRndt, where CRni-1+ represents radon concentration remaining after decay in the residual layer from the previous afternoon. An approximation of linear decrease in CRni-1+ with height was considered (Williams et al., 2011), reaching radon concentration of zero at the top of the previous day's residual layer. When MLH reaches its full extent in the late afternoon, it can extend above the previous day's residual layer, thus incorporating Rn “free” air into the ML.

The second part of modelling uses the box model (Eq. 1), where measured BC concentrations, apportioned to sources, are inverted, taking into account effective MLH determined during the first step, to calculate hourly resolved BC emission rate (EBC).

The 1 min dataset of source-apportioned BC concentration was first averaged to a 1 h time base in order to correspond to the determined MLH values. BC emission rates were calculated separately for traffic (ETR) and biomass burning emissions (EBB), using Eqs. (11) and (12), for increasing and decreasing MLH, respectively: 11EBC=1ΔTBCCBCihi-CBCi-1hi-1e-λBC′dt-CBCi-1+hi-hi-1e-λBC′dt,12EBC=hiΔTBCCBCi-CBCi-1e-λBC′dt, where the index i represents the traffic (TR) or biomass burning (BB) contributions to BC concentrations, and λBC′ is the decay constant calculated by Eq. (3), which accounts for temporal decay and horizontal advection. The latter is introduced due to dispersion characteristics and inhomogeneous spatial distribution of emission sources, which usually leads to a decrease in species concentration downstream. In the Eulerian box model, the difference between species concentration within the modelled area and outside the box controls the spatial decrease in the concentration downstream. Based on the study presented by Williams et al. (2016), an assumption of exponential decay was considered in this study to simplify the model and overcome the missing measurements at the outer box limits. The size of the modelled area and distribution of specific sources lead to source-specific spatial decay constants, namely γBB for biomass burning and γTR for traffic-related BC. Spatial decrease in BC concentration with distance from the source for different choices of γ is presented in Fig. S13a.

Since BC particles are inert, the rate of BC removal from the atmosphere is governed by wet deposition (e.g., Blanco-Alegre et al., 2019). The temporal sink was estimated based on mean lifetime of soot particles in the atmosphere, which can be considered between 1 week and 10 d (Cape et al., 2012). Therefore λBC of 0.006 h-1 was considered in this study, corresponding to 1-week mean lifetime of BC. The same temporal sink was considered regardless of BC source.

Data analysis and graphical representation were performed using the R programming language (R Core Team, 2018), with the “ggplot2” (Wickham, 2009), “openair” (Carslaw and Ropkins, 2012), “dplyr” and “deming” packages. If not stated otherwise, time is reported as local time (CET/CEST). Seasonal statistics was computed considering December–February as winter, March–May as spring, June–August as summer and September–November as autumn.

Average radon activity concentration derived from hourly measurements (Fig. 2) was similar at both measurement locations, 15 ± 11 and 14 ± 10 Bq m-3 in winter and 13 ± 9 and 12 ± 8 Bq m-3 in spring, in Ljubljana and Vipava valley, respectively (Table 4). Note that radon measurements were performed at different heights above ground: 1 and 3 m in Ljubljana and Vipava valley, respectively, which affects average concentrations. These values are above the annual average outdoor radon concentration of 10 Bq m-3 reported by UNSCEAR (2000) for the continental areas. Due to limited atmospheric mixing, higher winter concentrations are usually observed. However, a decrease in atmospheric CRn by more efficient atmospheric mixing is compensated for by increased radon exhalation rate in the warmer season.

Apart from the changes in radon exhalation rate from the ground, time evolution of CRn is mainly affected by atmospheric dispersion characteristics. Periods of mechanically driven mixing within the PBL, with stronger wind speeds, and periods of prevailing thermally driven mixing can be distinguished in particular during winter months, which results in irregular diurnal time evolution. Typical diurnal variation is more pronounced in spring, when thermally driven atmospheric mixing prevails. Due to the limitations of the box model, this study is limited to the cases with a thermally driven convective boundary layer. With this in mind only days with average daily wind speeds below 2 m/s were considered and addressed further on as “normal” wind conditions. Local wind conditions are further presented in the Supplement (Sect. S3, Figs. S4 and S5). Diurnal variation in CRn in thermally driven convective mixing, presented in Fig. 3, reflects daily evolution of the PBL with the lowest CRn in the middle of the day, when PBL is fully mixed. The lowest values of CRn are on average around 5 Bq m-3. CRn starts to increase with the afternoon transition to the stable boundary layer and reaches the highest values in the early morning. The amplitude of diurnal variation is controlled by PBL stability and duration of SNBL, resulting in the highest morning peak values in winter months, when the SNBL regime lasts longer.

Clear seasonality of BC concentrations was observed at both urban background sites. Higher concentrations were measured in the colder season (Fig. 4), resulting from weaker dispersion characteristics within the more stable PBL, as well as from stronger biomass burning sources.

The average BC concentration in winter was 4.5 ± 5.7 and 3.4 ± 4.2 µgm-3 for LJ and AJ, respectively (Table 4). However, a significant micrometeorological difference between both locations has to be considered. Vipava valley is characterized by two extremes in atmospheric stability: very stable atmospheric conditions with strong pollution events can shift within a few hours to the strong bora wind conditions, which disperse all atmospheric pollutants to the nearly regional background levels. In fact, during stable PBL conditions in winter, BC concentration in AJ can easily exceed concentrations in LJ, reaching an average daily BC concentration of 10–15 µgm-3. Based on the source apportionment model described in Sect. 2.2, there was a significantly higher contribution of biomass burning observed during winter in AJ (62 %) than in LJ (31 %), corresponding to the rural characteristics of the Vipava valley area. Significantly lower BC concentrations were measured in spring, 1.5 ± 1.6 and 1.1 ± 1.2 µgm-3 in LJ and AJ, respectively.

BC concentrations at both hill sites were expectedly lower than that at the urban background sites. The Golovec site (GOL), which is located 100 m above the city of Ljubljana is nevertheless more affected by urban emissions than the Otlica site (OT), which lies about 830 m above the valley floor. BC concentrations measured at GOL were 2.2 ± 2.0, 1.1 ± 1.0 and 0.8 ± 0.5 µgm-3 in winter, spring and summer, respectively, which is 51 %, 42 % and 38 % lower than in the city. This indicates more intensive vertical dispersion of air pollutants (including BC) towards the warmer season. Nevertheless, since the vertical difference between ARSO and GOL site is only 100 m, the GOL site remains above the ML only during very stable PBL conditions.

On the other hand, the vertical difference between the AJ and OT sites in Vipava valley is much larger, resulting in significantly lower BC concentrations on the hill. BC concentrations measured at OT during autumn, winter and spring were similar, 0.4 ± 0.5, 0.6 ± 0.8 and 0.4 ± 0.4 µgm-3, respectively. Slightly higher winter concentrations can be assigned to small local contribution from a few houses which are spread on the slope around the observatory and a small natural grass fire close to the observatory on 18 December 2016, which increased BC concentrations to around 30 µgm-3 for several hours (Fig. 4). The OT site is located above the PBL most of the time during winter and therefore represents regional background BC concentrations. Towards spring, when MLH frequently reaches the OT site in the afternoon, the site is affected by polluted air masses from the valley (Fig. 8c) and BC concentrations increase. The OT site can lie during the night and morning hours in either the residual layer – in the case when MLH reached the OT site in the previous afternoon – or in free atmosphere, in the case when MLH remained below OT altitude on the previous day.

The BC diurnal variation presented in Fig. 5 reflects different dynamics of sources and their relative contribution. In general, the main driver of BC concentrations at both sites is atmospheric stability, leading to dispersion of pollutants during the day, and subsequently lower BC concentration in the middle of day, and thus lower exposure of the population, except in the case of stable PBL conditions. In addition, two peaks are usually observed in traffic-related BC concentration (BCTR), which is a combined consequence of traffic density and PBL stability. The morning traffic-related peak of BCTR concentration is usually stronger at both locations, since dispersion of BC in the morning hours is limited due to low MLH. Due to higher traffic density and consequently stronger BC sources in LJ, it usually takes more time for BC to decrease during the day than in AJ. The afternoon peak, on the other hand, strongly depends on daylight hours (which in general drive the PBL evolution). In winter, BC concentrations start to increase already between 16:00 and 17:00, whereas in spring and summer, a much smaller increase can be observed, which is constrained to evening hours. Biomass burning BC sources are mostly limited to the colder season, when higher concentrations are measured, especially in the evenings and the first part of the night. In contrast to LJ, AJ is also affected by increased BCBB concentration during the morning hours. During the weekends, lower BCTR concentrations are observed in LJ, whereas no significant difference can be seen in AJ, leading to the assumption that meteorology plays a much stronger role in Vipava valley than it does in Ljubljana (where BC sources are stronger), or it could be assumed that the highway along the valley represents a continuous source of BC, regardless of the weekday.

Hourly resolved MLH values were calculated based on Eqs. (6), (8) and (9) for the whole period, when CRn measurements were available. Although MLH results represent an intermediate model outcome and are actually not required for emission rate modelling, the results are important for understanding diurnal characteristics of PBL evolution and extent of pollutant dispersion, which allow us to compare the two locations from the point of view of micro-meteorological characteristics. They also serve as a quality control parameter of the model. Derived MLH for both locations, calculated from the specifically selected monthly values of effective radon exhalation rate (Sect. 2.5), is presented in Fig. 6. SNBL height was in general between 100 and 200 m a.g.l. at both locations and was found to slightly increase from the cold to warm seasons. However, the seasonal pattern of SNBL height is not as pronounced as the seasonal pattern for the thermally driven daytime MLH. In February PBL reached its highest altitude at around 15:00, with the median MLH value for LJ of 450 m. On the contrary, in June MLH reached its highest extent of 1210 m (median) at 17:00. In conditions of an extremely unstable boundary layer, the maximum observed MLH extended higher than 2000 m at both locations. The influence of MLH on BC concentration measured at the urban background site (ARSO) and on the hill (GOL) is presented in Fig. 7 for selected days, when derived MLH was validated from vertical profiles of BC concentration measured by plane. The highest BC concentrations at ARSO and the highest difference between ARSO and GOL are observed during periods when MLH extends below the altitude of the hill site, 100 m a.g.l. (Fig. 7a).

The most stable PBL conditions (excluding periods of bora wind) in the Vipava valley were observed in December 2016 and February 2017, when no significant diurnal variation could be detected. During these 2 months median MLH values at 15:00 were 240 and 330 m, respectively. The highest vertical extent of PBL was observed in April, when MLH reached 1400 m (median) at 16:00. Results of MLH values also explain the measured BC concentration in AJ and OT (Sect. 3.2), where comparison of BC concentration reveals the time periods, when both sites are located within the same air volume (i.e., periods when MLH overreaches the OT site at 830 m a.g.l.). Especially in April and May, MLH reaches the OT site in the afternoon frequently (from noon to 16:00), leading to an increase in BC concentrations at OT and decrease in BC concentrations at the AJ site (Fig. 8b and c). Good correlation was observed between MLH (derived from the box model) and vertically resolved lidar backscatter signal over Vipava valley in periods when conditions are met for the application of both approaches. Figure 8a represents measurements from 9 January 2017.

Results show that the PBL reaches its full depth in the early afternoon, between 15:00 and 17:00, depending on the extent of daylight hours. Strong thermally driven mixing starts to diminish about 2 h before sunset, followed by rapid transition to the SNBL conditions (Fig. 6).

BC emission rates were determined in the second phase by inversion of BC concentrations based on the results of derived MLH values using Eqs. (11) and (12). Emission rates from traffic (ETR) and biomass burning (EBB) sources were determined separately in order to take into account spatial characteristics and different dynamics of sources. Average daily BC emission rates in different seasons for both locations are presented in Table 5. As expected, higher BC emissions are characteristic for Ljubljana, where overall BC emission rates ranged from 210 to 260 µgm-2h-1 in spring and winter, respectively. Lower overall BC emissions were found in Vipava valley and were in the range from 150 to 250 µgm-2h-1 in spring and winter, respectively. Emissions from traffic prevail in the city of Ljubljana and account for 73 % in wintertime. On the other hand, biomass burning in individual houses contributes more than half (60 %) of the emitted BC in Vipava valley during the heating season. In spring, however, outdoor temperature increases faster in the Mediterranean climate of Vipava valley than it does in Ljubljana, which means that the heating season ends much sooner in spring, resulting in only a 27 % contribution of biomass burning emissions in the Vipava valley and 14 % contribution in Ljubljana. The fraction of source-specific emission rates slightly differs from the contribution fraction of actually measured BC concentrations from both sources (Table 4) after mixing and dispersion within the PBL. Due to the difference in daily dynamics of emission rate from biomass burning and traffic, the fraction of BC concentration from biomass burning is slightly higher than the fraction of its emission rate. Traffic emissions occur mostly during the daytime and are dispersed in the PBL more effectively than biomass burning emissions, with the sources also active during the night hours, thus having a stronger impact on the concentrations. Average determined BC emission rates are about an order of magnitude higher than Slovenian national BC emissions of 2.2 kilotons reported by the EMEP (The European Monitoring and Evaluation Programme) emission inventory for 2016, which corresponds to the average hourly emission rate of 12.4 µgm-2h-1. The difference is reasonable if we account for spatially heterogeneous emissions and the small contribution of less populated areas like forests and mountains. BC emission rates calculated in our study are nevertheless lower than reported for larger cities, such as Kathmandu, where 316 and 914 µgm-2h-1 were reported for the summer and winter periods, respectively, or Delhi (608 µgm-2h-1) and Mumbai (2160 µgm-2h-1 ) (Mues et al., 2017).

Daily average ETR remains constant through the year and in general does not depend on outdoor temperature (Fig. 9). As expected, EBB is higher on colder days due to the stronger heating demand. Since wood is the most frequently used fuel for heating in individual houses in the Vipava valley, emission rate increases much faster with colder days than it does in Ljubljana, where parts of the city dominated by individual houses are connected to the district heating system powered by the local thermal power plant. At both locations, higher EBB is observed when average daily temperature drops below 15 ∘C.

The uncertainty of the box model depends on different parameters and processes.

The results of MLH determined by the box model strongly depend on the correct (a) estimation of the radon exhalation rate. A biased effective ERn estimate would bias results of the EBC in a positive or negative way. Due to seasonal changes of the ERn, it has to be evaluated for each season and month separately. Since continuous monitoring of ERn is usually not available, the box model has to be calibrated to any available information on the MLH in order to get the ERn, scaled for the measurement height. In this regard it has to be pointed out that additional measurements, which can be used to determine the MLH for limited time periods, are necessary to lower the uncertainty of the ERn estimate. The uncertainty of the ERn was estimated to be 50 Bq m-2 h-1 (∼ 20 % of the mean ERn estimate for the area under investigation). To account for this, the model was evaluated for upper and lower ERn estimates which were selected 100 Bq m-2 h-1 apart (Table 2).

Uncertain levels of the (b) Rn concentration in the residual layer and approximation of its vertical gradient can influence the modelled daily evolution of MLH, especially towards the midafternoon, when the denominator in Eqs. (11) and (12) limits towards zero, making the box model highly uncertain. The uncertainty of the Rn concentration in the residual layer is estimated to be ∼ 50 %. However, the uncertainty of the MLH results increases with decreasing radon concentration in the mixing layer, when the resulting difference of Rn concentration between mixing and residual layer approaches zero. This reflects 50 %–75 % uncertainty of the MLH calculation in the midafternoon of convective days in the worst-case scenario. On the other hand, the residual layer Rn concentration does not influence the MLH estimates in the SNBL conditions.

As discussed in Sect. 2.6.1, (c) horizontal advection, which is accounted for by introducing spatial decay constants to the box model, can lead to an overestimation of the EBC, when advection prevails over the convective mixing. This effect is again present mostly during the midafternoon and adds to the uncertainty of emission rate estimation. The uncertainty of BC spatial decay constant is estimated at ∼ 30 %, where a 30 % increase in the spatial decay constant results in a 30 % increase in BC emission rates at midafternoon in the case of Ljubljana (on average).

Another contribution to the uncertainty arises from Rn measurements, when radon concentration, especially in the convective PBL, reaches the (d) instrumental lower detection limit in the early afternoon. This can lead to underestimation of the MLH and consequently also underestimation of the derived BC emission rate.

Uncertainty contributions described above lead to the conclusion that the highest uncertainty of emission rate estimate can be expected in the midafternoon period during the convective days, when the overall uncertainty can reach 100 %. On the other hand, the model uncertainty is the lowest in stable atmospheric conditions, when the main sources of uncertainty come from points (a) and (b), resulting in ∼ 30 % uncertainty of the BC emission rate estimates. The comparison of the traffic-related emission rate ETR and the traffic density in LJ shows the presence of the higher model uncertainty (overestimated emissions) in the midafternoon (Fig. 12).

Negative hourly EBC values result from the BC distribution, from a temporal and spatial point of view, not complying with the expected background evolution of BC concentration. Thus, the local BC concentration peak, measured at the urban background site, would result in a high calculated emission rate, followed by a negative calculation of the emission rate. This effect (positive–negative spike due to local BC concentration peak) is usually observed in the time period when sources are active. Higher noise is thus obtained during unstable atmospheric conditions in the presence of local BC concentration peaks. The traffic BC emission rate results in more noisy results than biomass burning BC emissions. Higher noise is also observed for the Vipava valley emission rate calculation, induced by non-homogeneous distribution of biomass burning sources. Negative values were treated as valid model results, since averaging removes these oscillations and results in a more realistic estimation of the emission rate.

Due to different BC sampling height at the LJ and AJ locations – 4 and 12 m, respectively – some uncertainty of BC emission rates can be expected during the SNBL conditions, since stratification of SNBL can play a role in measured black carbon concentration. This is especially important when comparing traffic and biomass burning BC sources, since their emissions have different characteristics. BCTR is emitted from the sources at the ground surface, whereas biomass burning sources are usually several metres higher, at the height of the chimneys. Due to dispersion and dilution processes, the concentration gradient flattens with time. Thus, in the case of traffic-related BC with higher intensity during the day, there would be enough time for the dispersion of BCTR before stratification of SNBL. However, the morning emissions before the break of SNBL could be slightly underestimated in AJ, where sampling was performed at 12 m above ground. On the other hand, biomass burning BC is emitted higher above ground. For the Ljubljana basin it was shown that BCBB is homogeneously distributed within the city (Ogrin et al., 2016). At the AJ location, with numerous biomass burning sources over a smaller area, the concentration profile could be more significant, especially in stable atmospheric conditions, which could lead to increased BCBB measured for the same level of emissions. This could in turn cause slight overestimation of EBB in the afternoon–early evening, before the emission plume is dispersed. However, a rough estimate of the emission inventory leads us to believe that biomass burning is ubiquitous in AJ, not leading to significant emission gradients in the urban area.

Overall, the box model results are more reliable in stable atmospheric conditions, especially during the morning hours, after the break of stratified SNBL and before midafternoon advection prevails in the convective mixing. To account for the uncertainty, the midafternoon MLH estimates were excluded from the ERn calibration procedure, and weighted averaging was used to determine the daily average of BC emission rates. Measurements of pollutant concentration should be conducted at background sites, to allow for their homogeneous dispersion, resulting in lower noise of the calculated emission rates.