Introduction

Due to its adverse effects, air pollution is one of the biggest challenges for urban areas. Every year, exposure to pollutants such as particulate matter (PM), ozone (O3), NO2, SO2, and CO causes millions of health issues worldwide [1]. The primary sources of these pollutants are vehicles and burning of fossil fuels for heating and power generation [2]. The air quality over an urban area depends not only on the emission source but also on dispersion conditions in the atmospheric boundary layer (ABL) which are driven by meteorological parameters (e.g., temperature, wind speed, precipitation). The lower part of ABL is called the mixing layer (ML), which is directly affected by the Earth’s surface and responds to surface forces on a time scale of one hour or less [3]. Its height typically ranges from a few meters to several kilometers and is considered to be a crucial parameter controlling the dilution and accumulation of pollutants concentration near the ground [3, 4]. After the sunrise, pollutants released within this layer are dispersed by mechanical turbulence and convection generated by the solar radiation. After the sunset, the earth's surface cools down, the temperature inversion occurs, and the turbulent mixing near the ground becomes attenuated. As a result, all substances, including pollutants, accumulate in a stable layer of air adjacent to the ground.

Several techniques have been developed for characterization and determination of mixing layer height (MLH). The conventional methods include meteorological radiosonde, ground based remote sensing (sodar, lidar, doppler radar) and aircraft surveys, but to this day it is still a challenge to determine the MLH in an automated way with good resolution. As reviewed in Seibert et al. [5], the radiosonde-based method provides high quality data, but due to its high cost, only two observations can be made throughout the day, and its vertical resolution is also limited. On the other hand, aircraft profile measurements provide high resolution data but due to weather conditions, security constraints and high cost, such measurements are limited to only short time periods. Ground-based profile measurement methods (e.g., sodar, lidar, Doppler/wind profiler) methods are promising methods that provide reasonable information; however, their resolution is limited, especially for low levels of MLH [5].

To overcome these problems, an alternative way of assessing MLH was proposed. Utilizing the so-called box model, it is possible to calculate the MLH based on the concentration of 222Rn (radon) near the ground. Radon is especially suitable for this purpose because as a radioactive noble gas, it is chemically non-reactive, and its concentration can be measured with high accuracy even though radon is present in the atmosphere only in trace amounts. Radon half-life is comparable with the residence time of major atmospheric compounds and synoptic time scales. It is also short enough to reflect the temporal changes in local atmospheric conditions [6, 7]. The main source of radon in the atmosphere is soil and rocks, and the change in its concentrations mainly depends on atmospheric mixing and its flux [8]. Since the temporal changes in radon flux are negligible compared to those caused by atmospheric mixing, it is considered a good indicator of atmospheric mixing [9, 10]. For the abovementioned reasons, radon is a suitable atmospheric tracer (e.g., [11, 12]). The so called radon tracer method has been employed by many authors to estimate the flux of greenhouse gases [13,14,15,16]. Radon also has been used in the studies dealing with the transport of air masses (e.g. [17, 18]). Other researchers used atmospheric radon to study atmospheric stability (e.g. [19,20,21]), and observed that compared to conventional method of stability classification (Pasquill–Gifford classes), the radon-based method distinguishes the trends of air pollutants better. For the determination of MLH, a box model based on outdoor radon was originally developed by Fontan et al. [22]. This model was further improved upon by Sesana et al. and Vecchi et al. [23, 24], and was employed in many other studies [25,26,27,28,29]. The results were found to be in good agreement with those obtained by other, more conventional methods, such as sodar and lidar.

The influence of MLH determined by different approaches on pollutant concentration have been investigated in various studies that were conducted mainly in the urban areas. A comprehensive study in different locations in China was performed to investigate the relation between MLH measured by lidar and PM2.5, and found a negative correlation in most cases [30]. Similarly, in different cities around the world, a significant anticorrelation was observed between the concentration of pollutants (PM, CO and NO2) and MLH retrieved by different methods, mostly by ground based remote sensing methods utilizing lidar, sodar, ceilometer or radiosonde (e.g. [31,32,33,34,35,36,37,38,39,40]).

Many studies observed a clear correlation between MLH and O3 [36,37,38,39]. However, the relationship between MLH and O3 is not clearly established. For example, it was observed that shallow MLH caused high O3 concentrations due to pollution accumulation near the ground, resulting in efficient O3 production in North China [41]. Although most of the studies found a negative correlation between MLH and primary pollutants (e.g., PM and CO) and positive correlation between MLH and secondary pollutants i.e., O3, the level of significance and even the sign vary significantly with location and season. Therefore, as of now, it is still difficult to draw a solid conclusion on the relation between MLH and pollutant concentration. According to Geiß et al. and Wagner et al. [38, 39], both the method of MLH retrieval and the way the data are statistically analyzed plays an important role in the assessment of pollutants behavior. For instance, Schäfer et al. [33] used the daily mean values of pollutant concentration and MLH for statistical analysis, while Wagner et al. [39] analyzed grouped data for the same region in Germany. The grouped-data approach resulted in a stronger correlation between the MLH and pollutant concentrations. Both Wagner et al. [39] Rost et al. [40] recommend the use of the Sturges grouping method for correlation studies.

To date, there is still an ongoing debate regarding the best method of MLH retrieval and subsequent statistical analysis with urban pollutants. This study presents the results of MLH calculated from outdoor radon measurements in Bratislava, Slovakia, covering the years 2020–2021. This is the first time the radon-based MLH has been analyzed and related to the concentration of air pollutants in this region, employing diverse statistical techniques. In addition, this work seeks to make two additional contributions to the field of atmospheric science:

  1. (1)

    Unlike previous studies on radon-based MLH which assumed the radon exhalation rate to be constant throughout the year, this study considers seasonal variation of radon flux obtained from the European radon flux map based on GLDAS-Noah v2.1 soil moisture data [41]. From this dataset, the daily mean values of radon flux corresponding to our measurement site (Bratislava, Slovakia) were extracted and used for MLH calculations.

  2. (2)

    To the best of our knowledge, comparisons between the radon-based MLH and other methods of MLH retrieval are scarce in the literature. In this paper, we compare radon-based MLH with the boundary layer height based on the Richardson number which is available at the European Centre for Medium-Range Weather Forecasts [42]. The analyzed boundary layer height data consisted of hourly values filtered for our location and were evaluated in the same way as the radon-based MLH.

Methodology

Radon and pollutant concentration measurements

Continuous measurement of radon activity concentration (RAC) was performed using two independently calibrated scintillation detectors on the campus of the Faculty of Mathematics, Physics, and Informatics of Comenius University in Bratislava, Slovakia for 2 years (2020–2021). The detectors were placed around 220 m apart (Lat: 48○ 9′ 4″N; Lon: 17○ 4′ 14″E and Lat: 48○ 9′ 8″N; Lon: 17○ 4′ 3″E, respectively). The principle of operation for both detectors is the detection of scintillation signals ejected from the inner walls of the detectors due to absorption of alpha particles emitted by radon and its progeny. The active volumes of the scintillation chambers are 2.25 L (LSCH) and 1.0 L (SCH1L), respectively. Air is sampled from a height of 1.5 m through a PVC pipe and pumped to the detection system at a flow rate of ∼0.5 L min−1. At the entrance to the chambers, the air passes through a filter. In this process, aerosols and radon progeny are removed. A 5 L and 10 L (for SCH1L and LSCH, respectively) delay volume was incorporated in the intake lines to ensure that the air entering the chambers will no longer contain thoron (220Rn) with a half-life of 56 s. Detected count rates are automatically recorded and stored in a computer's memory. Subsequently, radon activity concentrations belonging to 2 h intervals are calculated using the Ward and Borak method [43].The Ward and Borak method is based on the determination of the so-called normalized detector response function, which characterizes the response of the detector to radon-laden air over time. This response function incorporates the effect of all detector parameters and operating conditions such as flow rate, humidity, counting efficiency, detector volume and plate-out effect, thus eliminating the need to estimate these effects independently.

The detector calibration procedure is as follows: for the first measurement interval (2 h in our case), air with a known RAC is drawn through the detector. The detector count rates in this interval increase rapidly due to the increased RAC within the sensitive volume of the detector as well as due to associated buildup of radon progeny within the volume and at inner surface of the detector. At subsequent intervals, radon-free is passed through the detector. In these subsequent intervals, detected count rates gradually decrease to background levels as 222Rn and its decay products are flushed from the detector volume and radon progeny deposited on the detector inner walls are allowed to decay. The calibration outputs are the τi coefficients; their mathematical derivation is described in detail in the original study [43]. The resulting formula for calculating the radon activity concentration A(t) is:

$$A\left( t \right) = \tau_{0} \left( {N_{0} - N_{B} } \right) - \mathop \sum \limits_{i = 1}^{m} \tau_{i} \left( {N_{i} - N_{B} } \right),$$
(1)

where N0 is the detected gross counts in the last measuring interval, NB is the detector background rate and Ni are the detected gross counts in the previous intervals. Since the absolute values of τi coefficients for higher values of i approach zero, it is sufficient to consider up to 4 preceding intervals, e.g. m = 4.

The lower limits of detection at the 95% confidence level [44, 45] are 2.8 Bq m−3 for LSCH (background count rate is 0.0166 s−1 and detector sensitivity is 0,0026 s−1/ 1 Bq m−3) and 3.5 Bq m−3 for SCH1L (background count rate is 0.008 s−1 and detector sensitivity is 0,0015 s−1/ 1 Bq m−3), respectively. This measurement systems allow obtaining almost 80% of outdoor radon activity concentration data with an error less than 30% [46]. To minimize the uncertainties related to RAC measurements, the data from two scintillation detectors were averaged. Since both detectors measure the RAC with approximately the same uncertainty, the final uncertainty due to the averaging the RACs is reduced by a factor of\(\sqrt{2}\).

The reliability of the detectors was tested by simultaneous measurements of RAC by LSCH, SCH1L as well as by a commercially available radon detector AlphaGuard, which served as an independent reference standard. The comparison took place during a period of two weeks in the summer of 2018 in a well-ventilated room, with RACs ranging from 10 to 70 Bq m−3 and exhibiting distinctive diurnal patterns. The time series of RAC obtained by all three detectors were almost identical; the corresponding linear regression coefficients for all combinations of detector pairs were on the level of R2 ~ 0.90.

The concentrations of air pollutants (i.e., PM10, PM2.5, CO and O3) were measured continuously at the stations located at Jeséniova street and Trnavské Mýto in Bratislava by Air Quality Department of the Slovak Hydrometeorological Institute (SHMI) [47]. Both the Jeséniova and Trnavské Mýto stations are located in downtown Bratislava and are about 2.5 km and 3.5 km apart from the university campus, respectively (Fig. 1).

Fig. 1
figure 1

a Location of the city of Bratislava, Slovakia within Europe. b Monitoring stations in Bratislava from which the data were collected

Full size image

MLH based on radon

For the determination of MLH, a box model based on outdoor radon concentration initially developed by Fontan et al. [22] and further improved upon by Sesana et al. and Vecchi et al. [23, 24] was used in this study. This model is based on the mass balance relation which assumes that radon exhalation rate remains approximately constant over short time intervals, outdoor radon concentration is not affected by horizontal movement of air, the concentration of radon at a given time is the same within the whole volume of the box, and the only way to remove radon from the box is through radioactive decay. The schematic view of the box model is shown in Fig. 2. The base of the box is located at the ground surface. The radon gas (222Rn) with the volume concentration \({C}_{i}\) [Bq m−3] and the surface emission rate \(\varphi\) [Bq m−2 s−1] enters a box of the height \({h}_{i}\) [m]. Within this box, radon is assumed to be homogeneously mixed. Mass balance relation (2) for the box model consists of three main terms (i.e., emission, legacy, and encroachment). On the right side of relation (2), the first term represents the emission part (i.e., radon is supplied to the box from the soil with exhalation rate \(\varphi\)), the second term is the legacy part (i.e., the height of the box measured after every 2 h). Finally, the last term represents the encroachment part and describes the situation when the MLH is growing, the mixing layer and the residual layer become coupled and as a result, the radon concentration remaining in the residual layer from the preceding day needs to be added to the box.

Fig.2
figure 2

The schematic view of the box model, having ground surface as its base, and mixing layer as its height (\({h}_{i}\))

Full size image
$${{C}_{i+1}h}_{i+1}=\frac{\varphi }{\lambda }\left(1-{e}^{-\lambda \Delta t}\right)+{{C}_{i}h}_{i}{e}^{-\lambda \Delta t}+{C}_{i}^{r}({h}_{i+1}-{h}_{i}){e}^{-\lambda \Delta t}$$
(2)

The initiation of this box model begins in the late afternoon when the MLH starts to shrink. To describe the complete diurnal cycle, three different conditions can be extracted from the mass balance relation:

  1. 1.

    When the MLH is shrinking (\({h}_{i+1}<{h}_{i}\)) (usually in the late afternoon), the residual layer becomes decoupled from the mixing layer (\({C}_{i}^{r}={C}_{i}\)) and from relation (2) it follows:

    $${h}_{i+1}=\frac{\varphi (1-{e}^{-\lambda\Delta t})}{\lambda ({C}_{i+1}-{C}_{i}{e}^{-\lambda\Delta t})}$$
    (3)
  2. 2.

    When the MLH growing (\({h}_{i+1}>{h}_{i}\)) (usually after the sunrise), residual layer containing a volume of air is incorporated into the mixing layer and the relation (2) gives:

    $${h}_{i+1}=\frac{\frac{\varphi }{\lambda }\left(1-{e}^{-\lambda\Delta t}\right)+{h}_{i}{e}^{-\lambda\Delta t}({C}_{i}-{C}_{i}^{r})}{{C}_{i+1}-{C}_{i}^{r}{e}^{-\lambda\Delta t}},$$
    (4)

    where \({C}_{i} \left[Bq{m}^{-3}\right]\) is the radon concentration corresponding to the odd hours of the day (1:00, 3:00, 5:00, …). However, since the algorithm for calculating the MLH would benefit from having more data points throughout the day, the original 2 h data on RAC were interpolated by the cubic spline method for each even hour of the day (2:00, 4:00, 6:00, …). This gives the MLH time series derived from the radon data will achieve a more realistic shape that better reflects local changes in atmospheric conditions, e.g. due to the time shift of sunrise and sunset throughout the year.\({h}_{i}\) [m] is the MLH at time \({t}_{i}\), \(\varphi [Bq{m}^{-2}{s}^{-1}]\) is the radon exhalation rate. In this study, the daily mean values of radon flux from the European radon flux map based on GLDAS-Noah v2.1 soil moisture were considered [41]. \(\lambda \left[{h}^{-1}\right]=0.0076\) is the radon decay constant, \(\Delta t={t}_{i+1}-{t}_{i}\) (i.e. 1 h in our dataset), \({C}_{i}^{r}={C}_{min}{e}^{-\lambda ({t}_{i+1}-{t}_{min})}\) is the radon concentration in residual layer and \({C}_{min}\) is the minimum radon concentration from the previous day.

    1. 3.

      If \({h}_{i+1}>{h}_{max}\) (\({h}_{max}\) is the maximum height recorded in the previous day), the condition 2 is modified as:

    $${h}_{i+1}=\frac{\frac{\varphi }{\lambda }\left(1-{e}^{-\lambda \Delta t}\right)+{h}_{i}{{C}_{i}e}^{-\lambda \Delta t}+({h}_{max}-{h}_{i}){C}_{i}^{r}{e}^{-\lambda \Delta t}}{{C}_{i+1}}$$
    (5)

    Without this modification, the model would add radon-free space in the box above the \({h}_{max}\), leading to uncertainty in the determination of MLH.

    Since this model is very sensitive to random fluctuations of RAC, the RACs measured every two hours were first smoothed by applying the Fast Fourier Transform filter (FFTF) which rejected periods lower than 8 h. Then, using relations (3), (4) and (5), the MLH was calculated, and the results were used to investigate the influence of MLH on the pollutant concentration (PM10, PM2.5, CO and O3) in Bratislava, Slovakia.

Correlation between MLH and pollutant concentration

For the correlation analysis, the data were grouped according to the Sturges method [48] to reduce the influence of other factors (e.g., emission rate, wind speed, and chemical reactions occurring in the atmosphere) on the air pollutant concentration. The Sturges method defines the optimal classification of data with the following relation:

$$C=\frac{R}{1+3.322\mathrm{log}N}$$
(6)

where C is the optimal class width, R is the range of data (i.e., the difference between maximum and minimum values) and N is the number of measured data. The denominator of relation (6) gives the optimal number of classes.

Results and discussion

Outdoor radon activity concentration

Monthly averaged composite diurnal cycles and mean values of RAC for each month of the year 2020–2021 are shown in Fig. 3. In 2020, the averaged RAC values ranged from the minimum of 4.4 Bqm−3 in February to the maximum of 10.3 Bqm−3 in January, and from 6.3 Bqm−3 in April to 10.7 Bqm−3 in November in 2021. The annual mean values of RAC in 2020 and 2021 were 7.9 Bqm−3 and 8.2 Bqm−3, respectively. While these values are lower than the annual average of 10 Bqm−3 for outdoor radon concentration reported by UNSCEAR (2000) [49], they are comparable to those obtained in other European countries [50]. Clear seasonal trends of amplitudes and mean values of RAC were observed during the measurement period. The typical composite diurnal cycle of RAC has an almost sinusoidal shape, with a maximum in the early morning and a minimum in the late afternoon. In addition to the seasonal variation of the radon exhalation rate, the diurnal and seasonal evolution of radon is mainly affected by atmospheric dispersion and meteorological parameters (e.g., solar radiation, wind speed and precipitation). Usually, maximum amplitudes with distinctive diurnal cycles of RAC are observed during the summer months (June–August) when atmospheric mixing is intensive due to strong thermal convection. On the other hand, weak atmospheric mixing due to reduced solar radiation in winter months (December-February) results in small and irregular amplitudes of RAC.

Fig. 3
figure 3

Composite diurnal cycles (0–24 h) of RAC for individual months of 2020–2021

Full size image

Radon-based MLH

Using the box model and a variable exhalation rate discussed in the Methods section, the MLH was calculated on an hourly basis. Figure 4 shows the temporal evolution of MLH against RAC in June 2020 and June 2021. On the level of individual days, when the RAC is low the MLH is high, and vice versa. In this study, the peaks of MLH above 2000 m were observed for RAC lower than 5 Bqm−3. In contrast, during the night the MLH often dropped to values as low as 100 m. When the MLH is shallow, the radon accumulates near the ground and its concentration increases. After sunrise, the MLH gradually increases due to turbulence and thermal convection caused by solar radiation.

Fig. 4
figure 4

Temporal evolution of MLH and RAC in June 2020 and 2021

Full size image

Figure 5 shows the box-and-whisker plot created from MLH data obtained in 1 h intervals for individual months of 2020 and 2021. A clear seasonal trend can be observed for each year. In 2020, the highest values of MLH occurred in May and lowest in January; in 2021, the highest MLH values were observed in July and lowest in December. Usually, the highest values of MLH were registered in spring and summer and lowest in autumn and winter. The seasonal variation of MLH is mainly governed by the surface heat flux [51, 52]. In this study, a strong positive correlation (\({R}^{2}=0.72\)) was observed between monthly mean values of MLH and surface net solar radiation data obtained from the ERA-5 reanalysis dataset of the Copernicus data store of European Center for Medium Range Weather Forecasts (ECMWF) [42]. Furthermore, as explained in [24], the temporal evolution of MLH may be related to the temperature lapse rate at the ground level. The authors observed that the increase in air temperature gradient from winter to spring is steeper than the decrease in temperature gradient from summer to autumn, which indicates that instability conditions occur more frequently in the springtime.

Fig. 5
figure 5

Monthly boxplots of MLH for the year 2020 and 2021. Horizonal lines, bars, and whiskers on the plot refer to median, 25/75 and 10/90 percentile of MLH, respectively

Full size image

The composite diurnal cycle of MLH averaged over two years (2020–2021) for four seasons of the year, i.e. spring (March–May), summer (June–August), autumn (September–November) and winter (December–February) is shown in Fig. 6. In each season, a clear diurnal cycle was observed. After the sunrise the MLH starts increasing, reaches its maximum between 14:00 and 16:00 and then gradually decreases till 20:00. The MLH remains almost constant during the nighttime (between 20:00 and 06:00). The height of this stable nocturnal mixing layer ranges approximately between 250 and 350 m. Seasonal differences in MLH during the nighttime are insignificant compared to those during the daytime. During the daytime the MLH is thermally driven, reaching its maximum of ~ 1350 m in spring and summer, ~ 950 m in autumn and \(\sim 650 \mathrm{m}\) in winter, respectively. Overall, these results are in good agreement with the typical diurnal cycle of MLH obtained in previous studies employing various methods of MLH retrieval, including the same method that was applied in the present study (e.g., [24, 29, 37]).

Fig. 6
figure 6

Composite diurnal cycles of MLH for four seasons of 2020–2021

Full size image

Comparison of radon-based MLH and ERA5-BLH

The mixing layer height obtained from outdoor radon measurements (MLH) was compared with the boundary layer height based on the ERA5 reanalysis dataset (BLH-ERA5). The BLH-ERA5 data were obtained from the Copernicus data store of European Centre for Medium-Range Weather Forecasts [42]. The BLH based on ERA5 is defined as the minimum height required for the bulk Richardson number to reach the value of 0.25 [53]. The analyzed data consisted of BLH data with the temporal resolution of 1 h filtered to our locality (Lat: 48○ 9′N; Lon: 17○ 4′E), and the data included years 2020–2021 (the same period for which radon-based MLH was calculated). Based on this data, composite diurnal cycles of BLH-ERA5 for each season of the year were calculated (Fig. 7), and can be directly compared to composite diurnal cycles of radon-based MLH shown in Fig. 6.

Fig. 7
figure 7

Composite diurnal cycles of BLH-ERA5 for four seasons of 2020–2021

Full size image

During the nighttime, the composite cycles of mixing height obtained by both methods are in good agreement, ranging between 250 and 350 m. The biggest difference is observed during the daytime, when the BLH-ERA5 increases more rapidly than the MLH. When compared to MLH, BLH-ERA5 overestimates the mixing height by up to 150 m. Apart from this, the seasonal variations of mixing height obtained by these two methods are very similar: the diurnal maxima occur between 14:00 and 16:00, and their values range from ~ 650 in winter to ~ 1500 m in spring and summer. In conclusion, apart from the different rate of increase after the sunrise, the seasonal composite diurnal cycles of the mixing height obtained by both methods are in very good agreement.

Monthly mean values of MLH and BLH-ERA5 are generally in good agreement, being lowest during the winter and highest during the spring and summer (Fig. 8). The largest differences are observed in spring and summer, when the monthly means of BLH-ERA5 are up to 200 m higher than those of MLH. A possible reason might be that the ERA5 overestimates BLH during the period of convective mixing, which was reported in another study [54]. Apart from that, a strong correlation (R2 > 0.8) was observed between MLH and BLH-ERA5 (Fig. 9).

Fig. 8
figure 8

Monthly averages of MLH and BLH-ERA5 for the year 2020–2021

Full size image
Fig. 9
figure 9

Monthly means of BLH-ERA5 vs. monthly means of MLH

Full size image

Relationship between MLH and pollutant concentration

The MLH is a crucial factor in modulating the pollutant concentration near the ground, in addition to the emission strength. It is important to know how the MLH affects the concentration of pollutants in order to assess the air quality in urban areas. The section below discusses the relationship between MLH and measured pollutant concentrations.

Diurnal cycles of MLH against pollutant concentrations (PM10, PM2.5, CO and O3) averaged over 2 years (from January 2020 to December 2021) are shown in Figs. 10, 11, 12. The PM concentrations (Fig. 10) reach their lowest values from around 03:00 to 05:00 and then gradually increase till 10:00. The PM concentration remains almost constant until late afternoon between 10:00 and 17:00, with a slight decrease around 14:00 when the MLH is at its maximum. After 19:00, the PM concentration gradually decreases until it reaches its minimum in the early morning. As the MLH starts increasing after the sunrise, one would expect to see a corresponding decrease in PM concentration due to more intensive atmospheric mixing. However, in the present study the PM concentration after the sunrise increased and then unexpectedly remained roughly constant throughout the daytime (Fig. 10). A possible explanation could be that atmospheric dilution caused by the growth of MLH was compensated by a corresponding increase in PM emissions, as also reported elsewhere [55]. Since PM is a mixture of primary and secondary pollutants, the production of secondary aerosols during the day contributes to the total amount of particulate matter in the air. This effect is particularly strong during the summer months when the photochemistry is quite intense due to increased solar radiation [56].

Fig. 10
figure 10

Diurnal cycles of MLH vs. PM concentration. The PM concentrations are averaged values from the stations Trnavské Mýto and Jeséniova

Full size image
Fig. 11
figure 11

Diurnal cycles of MLH vs. CO concentration. The acronym TM refers to the CO concentration measured at Trnavské Mýto station in Bratislava

Full size image
Fig. 12
figure 12

Diurnal cycles of MLH vs. O3 concentration. The acronym J refers to the ozone concentration measured at the Jeséniova station in Bratislava

Full size image

The diurnal cycle of CO exhibits a very distinct trend (Fig. 11) with two pronounced peaks during the day. CO is a primary pollutant with both natural and anthropogenic sources, originating mainly from incomplete combustion, biomass burning and oxidation of nonmethane hydrocarbons [57]. The minimum of CO concentration was observed in the early morning around 03:00. After that, the CO concentration rapidly increased, reaching its first peak at around 09:00. Due to the growth of MLH, the CO concentration decreased till the afternoon around 13:00 to 14:00. After that it started increasing, with a corresponding decrease in MLH. After reaching its second peak around 19:00, the CO concentration gradually decreased and finally reached its minimum level in the early morning. The observed peaks in the diurnal cycle of CO concentration in the early morning and late afternoon are likely related to the heavy traffic in those time periods, as also reported in [7]. Conversely, the low CO concentration occurring between 10:00 and 14:00 is likely caused by the synergic effect of less intensive traffic and atmospheric dilution due to the growth of MLH.

According to a report published by the Slovak Hydrometeorological Institute [58], the main sources of CO and PM in the Slovak Republic are the same (mainly traffic vehicles and fossil fuel combustion in households and energy sector). Hence, one should expect lowered concentration of these pollutants during well mixed atmospheric conditions occurring in the early afternoon. However, unlike the CO variation, the observed variations in PM2.5 and PM10 concentration are nearly constant during this period (Fig. 10). This implies that CO as a gaseous pollutant is dispersed more efficiently in the atmosphere than particulate matter. This is because PM is also affected by gravity, whereas gaseous pollutants are more influenced by diffusion [59,60,61].

Ozone (O3) is a secondary pollutant produced from its precursors (NOx and volatile organic compounds (VOCs)) in the presence of sunlight as a result of photochemical reactions. The concentration of ground ozone mainly depends on the concentrations of its precursors, intensity of solar radiation and the mixing processes [62, 63]. In the present study, the O3 concentration follows a diurnal pattern similar to that of solar radiation and MLH, being lower during the night and higher during the day. It reaches its minimum around 7:00; after the sunrise, it starts increasing and reaches its peak value at the same time as MLH does (between 14:00 and 16:00) Afterwards, its concentration decreases until its morning minimum (Fig. 12). The sharp increase in O3 concentration after sunrise is most likely caused by photochemical reactions and vertical mixing occurring in the atmosphere. Zhang et al. [63] noticed that during the early stages of MLH growth, considerable amount of ground level ozone is introduced into the mixing layer, i.e., ozone from the residual layer is forced to the ground, as the direction of ozone flux and momentum is downward during the day. In addition, the production of O3, as a result of photochemical reactions that are positively correlated with the intensity of solar radiation, gradually increases in the morning, reaches its maximum in the middle of the day and decreases in the afternoon. In the afternoon, the influence of photochemical reactions and vertical mixing diminishes, resulting in a gradual decrease in ozone concentration.

In order to quantify the relationship between the MLH and pollutant concentration, the data were processed by two different methods. In both cases, the data were fitted by a logarithmic function, which proved to match the observed trends better than a simple linear regression. The first method consisted of analyzing the daily mean values of MLH and pollutant concentration. Logarithmic regression analysis of these data yielded a weak negative correlation between the MLH-PM10, MLH-PM2.5 and MLH-CO datasets (\({R}^{2}=0.101\), 0.105 and 0.230, respectively), and a weak positive correlation between MLH and O3 (\({R}^{2}=0.12\)). These rather low R values are due to the fact that the concentration of atmospheric pollutants is not only affected by dispersion conditions within the MLH but also by other factors (e.g., source strength, wind speed, temperature). These results support the idea that since the daily mean data do not reflect the immediate changes in pollutant concentration induced by changes in MLH on the short time scales, it is inappropriate to use the daily mean values to determine the connection between MLH and pollutant concentration, as was reported in [39].

It is therefore useful to apply a second method, which consists of grouping the MLH data into classes to minimize the influence of other meteorological factors on pollutant concentrations. The number of classes and their width play a crucial role, therefore, the Sturges grouping method relation (6) was used to determine the optimal number of classes and optimal class width. Based on this method, the whole MLH dataset from January 2020 to December 2021 was grouped into classes for subsequent correlation analysis. Since the frequency distribution of MLH data is approximately exponential, dividing our data into classes of equal width results in much less data being in the higher classes compared to the lower ones. Therefore, classes containing the MLH data above 3990 m were excluded from this study. The 25th percentile, mean, median and 75th percentile of pollutant concentration for each class were calculated, and a logarithmic regression between the pollutants and MLH was performed. Figure 13 shows the boxplots of grouped MLH against pollutant concentrations. The results of logarithmic regression analysis for different percentiles including the mean values are summarized in Table 1. As can be noticed, a negative correlation exists between MLH and the concentration of pollutants (PM10, PM2.5 and CO), while the correlation between MLH and O3 concentration is positive. The correlation coefficient R2 depends on the quantile and the type of pollutant for which the logarithmic regression was performed, ranging from 0.34 to 0.69 for PM, from 0.69 to 0.93 for CO and from 0.87 to 0.96 for O3, respectively. Comparison of the correlation coefficients shown in Table 1 indicates that higher quantiles of PM2.5, PM10 and CO are more affected by MLH than lower quantiles. This may be because as the MLH shrinks, the primary pollutants accumulate near the ground, the pollutant concentration range increases and higher concentrations occur more frequently, leading to stronger correlation between MLH and higher quantiles of primary pollutant concentrations. Usually, the correlations are strongest for mean and median values of these pollutants. On the other hand, the correlations are strong for lower quartiles of O3 concentration and decrease slightly for higher quartiles. The correlations between MLH and mean concentration of all pollutants are significant (Table 1), ranging from the highest R2 values for O3 and CO to the lowest for PM2.5. This indicates that O3 and CO, being gaseous pollutants, are influenced more by the MLH compared to PM, which is also affected by gravity. Furthermore, the strictly non-linear relationship between MLH and O3 and CO indicates that these gaseous pollutants are most sensitive to the changes in MLH below 1350 m.

Fig. 13
figure 13

Boxplots of grouped MLH against the pollutant concentration. Horizonal lines, squares, bars and whiskers on the plot refer to median, mean, 25/75 and 10/90 percentile of MLH, respectively

Full size image
Table 1 Results of logarithmic regression analysis between atmospheric pollutants and MLH for the 3rd quartile, mean, median and the 1st quartile, respectively. The data were grouped according to the Sturges method
Full size table

Conclusion

The mixing layer height (MLH) plays a crucial role in understanding and modeling of air quality. In this study, MLH was determined using two years of continuously measured outdoor radon concentration data and daily radon flux extracted for our measurement site (Bratislava, Slovakia) from the European radon flux map. The typical diurnal cycle of MLH consists of a shallow and nearly constant MLH at night which gradually increases after sunrise, reaches a maximum in the afternoon, and finally decreases to stable values at night. As the MLH is thermally driven throughout the day, there is a clear seasonal difference in the evolution of MLH—a maximum of 1350 m is reached in spring and summer, 950 m in autumn, and 650 m in winter, with corresponding differences in the monthly averages of MLH.

The MLH calculated from outdoor radon and variable radon flux was then compared with the boundary layer height based on the ERA-5 reanalysis dataset (BLH-ERA5). Composite diurnal cycles of MLH and BLH-ERA5 for each season show similar seasonal variations. The largest difference was observed after sunrise, when the BLH-ERA5 increased more rapidly than the MLH. Monthly mean values of MLH and BLH-ERA5 showed good agreement, being lowest in winter and highest in spring and summer. The largest differences in mean values were observed in spring and summer, possibly due to the overestimation of BLH-ERA5 during convective mixing periods.

The relationship between several simultaneously measured pollutants (PM10, PM2.5, CO, O3) and MLH was investigated. The diurnal cycles of pollutant concentration plotted against MLH show distinct patterns and can be explained by their different physical properties and mechanisms of their formation. Grouping the MLH data into classes proved to be a superior method for correlation studies with atmospheric pollutants (as opposed to simply using daily means of MLH and pollutant concentration). Higher percentiles of primary pollutants showed stronger correlations with MLH, especially for mean and median values. Logarithmic regression provided the best fitting results, indicating a non-linear relationship between MLH and pollutant concentration.

These results, consistent with previous studies, confirm the effectiveness and efficiency of using MLH derived from outdoor radon concentration for air quality assessment. Radon-based MLH provides reasonable results and a straightforward, cost-effective alternative to conventional methods of MLH retrieval. The 2 year MLH dataset and its analysis with pollutant concentration provide unique and valuable information about the complex relationship between MLH and pollutants, which helps to interpret air quality in Bratislava, Slovakia. This dataset is also useful for policy makers aiming to reduce urban air pollution. Furthermore, our results contribute to a deeper understanding of the quantitative relationship between radon-based MLH, BLH-ERA5 and pollutant concentrations, which can be beneficial for atmospheric chemistry models and pollution monitoring and forecasting.