Analysis of Air Pollution Migration during COVID-19 Lockdown in Krakow, Poland

The historical analysis of particulate matter (PM) concentration proved that pro-clean-air legislation and grassroots movement have a positive impact on air quality in Krakow. However, when the temperature drops in late autumn, winter


INTRODUCTION
The problem of air pollution in Krakow has a long history. In the 1970s and 1980s, industry, mainly metallurgy, was one of the main air pollution factors. Over the years, as the population increased, the role of this factor decreased in favor of low emissions from fossil fuels heating and transportation (Bokwa, 2007). Krakow city's geographical location is well described in the literature (Morawska-Horawska and Lewik, 2003;Bokwa, 2019), as well as its geological structure (Rutkowski, 1989). The city itself cannot be considered in an isolation from the mesoscale landform features of the region. The general geographic information and urbanization relationships are described in the official Malopolska region strategy document (Urbanowicz et al., 2020) while the information about the near-surface geological structure has been the subject of many studies (Foldvary, 1998;Zaręba et al., 2020). Krakow is located in the valley. From the north, the elevation gain is related to Polish Jurassic Highland, on the south with limestone outcrops and Wielickie foothills. In a more mesoscale approach, going further south, there is the Carpathian inner-mountain basin and the Carpathian Mountains are just 100 km away (Gradziński, 1972). On the west Krakow borders with fault-block hills of Krakow Gate and Oswiecim basin, and from the west with Sandomierz lowland basin. The main river flowing through the city from west to east is the Vistula River (Hrehorowicz-Gaber, 2015). The latest research shows that thanks to pro-clean-air legislation, analysis methods and dedicated solutions allows for a much better understanding of many phenomena (Briggs et al., 2010;Hysenaj, 2016;Zaręba et al., 2019;Lupa et al., 2020). Based on previous research, Airly LCS accuracy in this period was very similar to the reference station measurements and this allows them to be used for geospatial analysis. It is important to know that LCS sensors need to be corrected according to the reference station measurements and weather-related conditions to provide reliable measurements of PM concentrations. On the other hand, the uncertainties of their measurements are greater than those of traditional measurements at reference stations, and their determination is more complicated (Peltier et al., 2021). Each Airly sensor is dynamically calibrated using factors generated by artificial intelligence (AI) and machine learning (ML) algorithms based on the specific characteristics of the particular location. Data that are available through their API for public use are already corrected according to the factors mentioned before. Airly is not sharing its calibration algorithms with the public (Airly, 2021b). However, the use of ML techniques for this purpose is well established and has been published in many papers (Zimmerman et al., 2018;Okafor et al., 2020;Wang et al., 2020), as well as discussed in the official World Health Organisation and World Meteorological Organization report (Peltier et al., 2021). It was also shown that during the COVID-19 pandemic spring the migration of air pollutions from solid fuels heating from surrounding municipalities to Krakow was the main source of PMs in the city as transportation was significantly reduced due to lockdown. Research made by scientists from AGH, commissioned by Krakowski Holding Komunalny (KHK) SA in Krakow, with the substantive support of the Voivodeship Inspectorate for Environmental Protection (WIOŚ) and the Chief Inspectorate for Environmental Protection (GIOŚ) and the financial participation of the Air Quality Department of the Municipal Office of Krakow and companies from the Miejskie Przedsiębiorstwo Energetyki Cieplnej SA and Miejskie Przedsiębiorstwo Komunikacyjne SA, showed that almost 50% of PM 10 consist of carbon fraction, 20% are inorganic secondary aerosols, the remaining ions are about 10%, 3-4% are metals, and the rest are unidentified components. Detailed studies of the isotopic composition of carbon proved that a major part of that fraction is coal. Its share and sources turned out to be varied due to the period of the year -from solid fuel heating -during autumn-winter-early spring period it is about 50%, while in the rest of the year it is about 20%. The share of transport traffic varied depending on the location and year period. During summer it was 32-42%, while during winter it was about 11-22%. The biogenic fraction part of carbon (natural emissions and biomass combustion) remains constant at around 30% (Voivodship Sanitary Inspectorate, 2020). Report of the National Center for Emission Management and Balancing, Institute of Environmental Protection -National Research Institute shows that 50% of emission sources of PM 10 and PM 2.5 in Krakow are related to non-industry solid fuel heating, 9% of sources are manufacturing processes, 10% are related with industry combustion process while agriculture is the source of only 4.6% of PM 10 pollution (Institute of Environmental Protection -National Research Institute, 2019). In our previous study including observations from the last 10 years, we showed also that pro-clean-air legislation in Krakow and grassroots movements helped to decrease average PM concentration in the city prohibiting the use of solid fuels heating. We also demonstrated the relation between relative comfort zone temperature (Jendritzky et al., 2001) and the level of PM 10 concentration from solid fuel heating in neighboring municipalities. We have shown that the feeling of cold determined based on the temperature measured by particular sensors at a given hour is a factor that allows identifying sources of pollution from solid fuels heating. For this purpose, we used spatial-temporal analysis of temperature and PMs concentration together with kernel density estimate of PMs and temperature concerning Predicted Mean Vote (PMV) and Perceived Temperature (PT) indicators (Jendritzky et al., 2001). We have indicated the places that were the main sources of air pollution transported to Krakow by diffusion during the spring lockdown in Poland (Danek and Zaręba, 2021).
In this study, our goal was to investigate the main sources of PMs pollution in accordance with wind direction and geographical location using a dense grid of Airly LCS. We wanted to examine the impact of particular towns and villages surrounding the city of Krakow not in a general way but with the use of categorization. According to Statistics Poland, Krakow has over 700,000 inhabitants while the number in the whole Krakow agglomeration (Krakow and surrounding municipalities) is close to 1.5 million (Statistics Poland, 2021a). Our goal was also to check whether there is not only spatial but also temporary evidence that pollutants emitted in neighboring municipalities are finally transmitted to the city of Krakow. The presented paper shows the unique use of a dense LCS grid for pollution migration during the COVID-19 pandemic period in a very specific region of Europe. Despite the very restricted air protection law, Krakow is still one of the most polluted cities in the world (Rogala, 2021).

METHODS
The experiments were conducted using a quasi-regular, dense grid of 90 Airly optical LCS (data available from: https://map.airly.org/, accessed on 28 September 2021). The free license of Airly allows for the use of no more than 100 sensors through their API. Sensors provided measurements of PM 1 , PM 2.5 , and PM 10 concentration, pressure, temperature, and humidity. Based on correlation analysis between PM 1 , PM 2.5 , and PM 10 (see Table 1) we decided to use in this study only PM 10 measurements as a good representative of air pollutions from solid fuel heating with a correlation coefficient with PM 2.5 equals 0.997 and with PM 1 equals 0.996. The comparison was made based on Airly LCS averaged measurements in March. There are also other motives for which the PM 10 fraction was selected for further analysis. EU standards for PM 10 concentration are significantly higher than for PM 2.5 , thus it is better to choose PM 10 while considering LCS as the accuracy for PM 10 measurement is about 20% of EU norm, while for PM 2.5 it is 50%. Another thing is that many reports and research done in the past were conducted on PM 10 concentration or PM 10 fraction analysis. It is also important that the PM 10 fraction contains information on all particles smaller than 10 microns including particles smaller than 2 microns. In light of these facts, it is reasonable to choose the PM 10 as a representative for further analysis. Because Airly sensors can be used by everyone who wants to buy them, the physical coverage of sensors' location in Krakow and neighboring cities is not regular. To provide the quasi-regular grid the custom algorithm in R was written. The k-nearest-neighbors method was used to find the sensors closest to the 100 point grid (in X and Y directions) and then the criterion of the quarter of the distance between particular sensors and grid points was used to decide if the sensors should be included or excluded. Data were collected hourly between 3 rd March 2021 and 16 th April 2021. The legibility of the PM measurements was proved by the time-series analysis of the government station and the Airly LCS (Danek and Zaręba, 2021). Manufacturer guarantee accuracy of Airly sensors for -PM 1 5 µg m -3 in the range 0-100 µg m -3 and 10 µg m -3 over 100 µg m -3 ; for PM 2.5 10 µg m -3 in the range 0-100 µg m -3 , 10% for measurements in the range 101-500 µg m -3 , and 20% over concentration 500 µg m -3 ; for PM 10 accuracy is the same as for PM 2.5 (Airly, 2021a). Sensor 36808 located in Niepołomice is the nearest to an official government PM 10 station located on 3 May Street in Niepołomice. Airly sensor 36808 measurements were averaged in a 24-hour window and plotted together with the government sensor measurements (see Fig. 1). The correlation coefficient between their measurements in the presented period was high -over 0.93 (Danek and Zaręba, 2021).
This period was chosen as it was the last strict lockdown in Poland. More or less strict lockdown regulations were in force from 8 th August 2020 to 24 th May 2021 with various changes during this period depending on the number of COVID-19 cases. Due to the rapid increase in infections numbers since the beginning of March, from 25 th March 2021 to 19 th April 2021, the lockdown was tightened (see in detail in the introduction). Krakow's labor market is dominated by employment in the IT, financial services, and education sectors (European Commission, 2021). It is known from the Central Statistical Office of Poland that most of these workers during the pandemic performed their work remotely without having to travel to their place of work (Statistics Poland, 2021b). Moreover, the number of students is almost 20% of the inhabitants of Krakow (Dębkowska et al., 2019). In the analyzed period, all of the mentioned above groups worked or learned remotely without generating car traffic. According to the official statement of  , 2020). Additionally, to minimize the impact of car traffic on the analysis of PMs concentration, the hours with the lowest car traffic were selected. Measurements of the traffic volume at the inlets to the city of Krakow, with particular emphasis on transit traffic done by Krakow city, showed that car traffic between hour 10 PM and 6 AM is minimal, while traffic is the greatest between 6 AM-9 AM and 1 PM-6.30 PM (Rosiek, 2017). The main sources of PM pollution in Krakow are low emissions from heating and car traffic (Traczyk, 2020). Selecting the lockdown period and hours in which, under non-pandemic standard conditions, the car traffic drops to almost zero, it made possible to observe pollutants from solid fuels heating only.
To choose days for directional air pollution inflow study the detailed analysis of PM maps was done (created in R using Thin-plane spline (TPS) interpolation method by Nychka et al. (2021)).
According to the WMO report (Peltier et al., 2021), the uncertainties of LCS measurements are higher than those for reference stations. According to the standard, the precision for gravimetric measurements is 2 µg m -3 (European Parliament, 2008), while for Airly sensors, the manufacturer declares it at the level of 10 µg m -3 for PM 10 . So it is five times lower. LCSs are sensitive to the influence of atmospheric factors, however, the data provided by Airly is already corrected, and the total uncertainty of individual sensors is not shared. The correlations of indications to the closest reference stations prove the high accuracy of the measurements (Fig. 1). In accordance with the LCS data processing standards specified in the WMO document (Peltier et al., 2021) for Level-4 (Schneider et al., 2019), we made continuous spatial distributions using the TPS method and analyzed the differences between these distributions and the indications of individual sensors. When analyzing a series of maps based on relatively sparse sensors network TPS has two important advantages over kriging. Firstly it does not require semi-variogram fitting thus different maps are directly comparable without any spatial model assumptions. Secondly, the TPS method is very resistant to separated anomalous sensor readings that can occur in sparse networks of LCS due to both measurement errors or the very local character of the observed phenomenon. This effect can be seen in the first map of Fig. 10 (2021-03-15 19:00) in Section 3.3.1 where four extremely high values were observed. The maximum residual value was equal to 184 mg m -3 (Table 2). But as for all these four sensors, the values from neighboring sensors were much lower the anomalies are not observed in the final map. Of course, these separated readings may represent the beginning of pollution emission but their point character makes them impossible for spatial interpretation. Please note that on the other maps such extremes have not been observed (Table 2). It is also worth noting, that increased residuals were observed only in the period when the onset of emission occurs (15-03 19:00 and 16-03 01:00) and not when the maximum pollution levels were recorded. It may indicate that these were not sensor errors but real point observations that have not yet propagated to neighboring sensors. The comprehensive distribution evaluation of PM together with humidity, temperature, and pressure were also performed to study other than wind and geomorphological conditions of PM migration. We used charts and cross-plots taking into account the differentiation by European Air Quality Index. The lag analysis was performed to study if the time dependency exists between higher emissions of PM in neighboring municipalities and Krakow city. First, the collected dataset was split into data from sensors outside and inside Krakow. Secondly, the sensors outside Krakow were split into groups depending on the main wind direction on a particular day. This allows for the examination of two-time series using the cross-correlation method. This makes it possible to objectively examine if there is a match between the distributions (between sensors group outside and inside the Krakow) and also to see the time difference. During the examined period the main wind direction was west. Only a few days have a dominant north wind direction. There were also days with the very weak wind where the direction was changing from hour to hour. These were classified as no wind days. For the group of sensors outside the Krakow city the following LCS

Pre-pandemic and Pandemic PM Concentration Analysis
Without a doubt, the COVID-19 pandemic changed the way we live. Restrictions altered our habits, the way we work, study, and travel. To examine its effect on general PM 10 concentration the 24-hour measurement from the official government mass station on Bujaka street in Krakow, from the last 4-years was plotted (see Fig. 3). It can be noticed that in general, the concentration of PM 10 in Krakow is decreasing year to year. It is related to law changes and grassroots movements that are present in Krakow since 2011 (Danek and Zareba, 2021). Fig. 4 shows the The main factor for PM 10 concentration in this month is the temperature. As mentioned before, the main source (over 50%) of PM 10 pollution in Krakow is solid fuel heating, so naturally, the temperature will have a dominant impact on its concentration. However, in this study, we wanted to examine the effect of PM 10 migration from solid fuel heating without additional background noise from car transportation (source of 11-22% depending on localization in the pre-pandemic year) which were limited during the lockdown. Summing up, the impact of the pandemic on the overall concentration of PM 10 in the atmosphere in Krakow is not dominant, however, it is crucial to eliminate the influence of the car transportation background. When analyzing the values in individual years in March, it is not possible to conclude unequivocally about the impact of the lockdown itself, as it is clearly visible that the dominant factor is temperature, which results directly from the specificity of heating houses in the region. Fig. 5 shows a graph for PM 10 , temperature, humidity, and pressure measurements for all 90 sensors in the whole investigation period. Fig. 6 demonstrates the relation between PM 10 concentration and other physical measurements in the context of the European Air Quality Index. Figs. 6(a) and 6(d) show the relation between temperature and humidity for Krakow city and neighboring municipalities. The relation between pressure and temperature is shown in Fig. 6 It is clearly visible that a higher concentration of PM 10 is strongly related to pressure. When the pressure was below 1005 hPa in the examined spring period, the air quality was good and no matter what the temperature values were. A similar situation is for humidity, only for neighboring municipalities some measurements gave a slightly worse index of air quality for humidity over 60% for pressure below 1005 hPa. The worst air quality index is for pressure range 1005 and 1015 hPa, but it changes in the range 1015-1020 hPa where the strong temperature dependence is visible (when dropping below comfort zone (Jendritzky et al., 2001). We can conclude that the highest concentration of PM10 is related to high pressure, low temperature, and high humidity, but with the dominant role of pressure (compare Ning et al. (2018)). These observations are in the line with Wilgosiński and Czerwińska's (2020) study about smog episodes in Poland. They proved that during the cold season high pressure is related to anticyclone circulation of very dry and cold air masses. During the night temperature drops significantly and during the day temperature increase. This situation leads to temperature inversion between cooler ground and warmer atmosphere. When the humidity is relatively low and the temperature is high, the PM10 quality index is good. However, this relation can be distracted by high pressure. This effect can be observed in Fig. 5 -on 29 th March, where is a relatively high temperature, low humidity, and high pressure and a noticeable higher concentration of PM 10 compared to the previous day where  pressure was much lower. According to Zhang et al. (2017) study, the effect of the humidity on PM concentration while atmospheric conditions are stable is low, however, relative humidity fluctuations can have a strong impact on pollutions concentration.

Relation between PM Concentration and Other Physical Atmosphere Parameters
To aggregate information from the regions of interest, namely west, north and Krakow groups we calculated daily averages and standard deviations of all available PM 10 readings from LCS stations in a particular group (see Fig. 7) and averages of meteorological factors (see Fig. 8). Results obtained for temperature, humidity, and pressure are nearly identical in all groups whereas PM 10 averages differ substantially. As expected readings from Krakow city are more similar to readings from the west group. This effect is cost by the dominant west wind direction. In general, values obtained for Krakow city are lower than those obtained for the west group, but in the days when the west wind is relatively stable and not too strong (e.g., March 16 th ) difference between these values disappears. Daily average uncertainties of PM 10 concentration measurements for Krakow and the north group are lower than those obtained for the west group. It may suggest more local character of emission in this group.

Analysis of Air Pollution Inflow Concerning Main Wind Direction
It has been shown that the migration of PM from neighboring municipalities to Krakow city, on days with no wind takes place by gravity fall or by diffusion as the city is located in the valley (Danek and Zaręba, 2021). Our goal was to check how the migration process of air pollutions depends on an additional external factor like the wind. During the studied period, the dominant wind direction was west (see Fig. 9). In the examined period the highest wind speed is related to wind direction SW. The south direction can be associated with a strong Foehn wind type which, under favorable conditions, may even have an impact on the regions of central Poland. This is a kind of warm and dry wind associated with the downwind slope of the mountain range (Marcinek et al., 2016). There were a few days with dominant north wind direction. For example, the good conditions for observation the inflow of PM10 to Krakow was the night between 15 th and 16 th March. In Fig. 5 it is clearly visible that those days are a part of days in the period when the increasing trend of pressure and decreasing trend of temperature with relatively high, stable   humidity are present. Furthermore, the temperature at the night is lower than in the next two days, even if the general 24-hour temperature is decreasing. The temperature on this night drop below comfort zone temperature and it is the main factor of increased heating of the households and therefore the main factor for generating air pollution as well. Fig. 10 presents maps of PM 10 inflow to Krakow city on the night between 15 th and 16 th March in hours: 19:00 15 th March; 01:00 16 th March; 02:00 16 th March; 06:00 16 th March. This is the time when car traffic in Krakow is close to zero. Additionally, the lockdown is a factor reducing population mobility resulting in reduced possible migration of pollutants generated by car traffic at other times of the day. As in Krakow and neighboring municipalities, two main PM sources are related to heating and transportation, we can conclude that the observed pollution is generated by solid fuels heating in neighboring municipalities. It is clearly visible that in the evening there is generally Fig. 10. Maps of PM 10 inflow with west dominant wind direction in the night between 15 th and 16 th March. White arrows indicate wind direction. Asterisks represent sensors' localizations, the blue line represents the Vistula River, red circles represent sensors with high residual value.

The inflow of pollution when the dominant wind direction is west
an increased level of PM 10 concentration in neighboring municipalities while the air in Krakow city beside Nowa Huta region is pretty good. After midnight, when the temperature dropped significantly the higher concentrations of PM 10 are visible in western regions. Wind speed is around 2 km h -1 . Fig. 11 shows the wind-rose diagram for the Krakow-Balice airport station (located on the northwest side of the investigated area) (calculated using https://mesonet.agron.iastate.edu/). In the next hour, the pollutants are transported to the city center through the Vistula River valley, to finally fill the city in a latitudinal arrangement around 6:00 16 th March. The distribution of isolines is latitudinal with the highest concentration of PM 10 along with the river line and the lowest to the south and north of this line. The local depression along the river valley, the higher humidity in this area, and the tendency to form mists create a favorable environment for trapping transported pollutants in this area. Fig. 12 shows a backward trajectory for 10 hours on that day for 3 different locations in Krakow agglomeration. The trajectories were calculated using READY (Real-time Environmental Applications and Display sYstem) provided by National Oceanic and Atmospheric Administration (Rolph et al., 2017). It is clearly visible that possible pollutant comes from the north and west surrounding of Krakow.   Average values of PM 10 concentration in the previous two days, and the following two days are noticeably lower. As mentioned before, mostly due to the minimal temperature value in the night between 15 th and 16 th March, which dropped around 0° Celsius. The lag between the maximum pollution point for west group sensors and the sensors in Krakow is visible. Fig. 14 shows the calculated lag value for those two time series for the same period as on the graph in Fig. 13. In general, the distribution for sensors in Krakow city is lagged about 1 hour compared to sensors in the west group.
3.3.2 The inflow of pollution when the dominant wind direction is north Fig. 15 presents maps of PM 10 inflow to Krakow city on the night and early morning on 18 th March in hours: 02:00, 03:00, 04:00, 05:00. Again we choose hours when the car traffic is very low and when the effect of households heating can be observed as the temperature is below the comfort zone (Jendritzky et al., 2001). We can say with certainty that the impact of PM sources other than those coming from heating is negligible at these times, especially during the period of partial lockdown with a relatively cold night. On that day around 02:00, Krakow and neighboring municipalities' air was very good. The situation started to change about 3:00 when the higher concentration of PM10 began to form in the northern area of investigated region. The dominant wind direction on that day was north and north-north-west. Fig. 16 shows the wind-rose diagram on 18 th March -again for the Krakow-Balice airport station. In the next hour the pollutions were transferred into the north region of Krakow city -to the Bronowice, Prądnik Biały, Prądnik Czerwony and Krowodrza. In the next hour, the pollutions were in the whole city and also in Wieliczka and other cities in the south of Krakow. For the rest of this day, there was no wind and the temperature was around 6-8 Celsius degrees. Later in the evening on this day, the effect of diffusion and gravity fall of pollutants into the city was shown by Danek and Zaręba (2021). Fig. 17 shows a backward trajectory for 10 hours on that day for 3 different locations in Krakow. The trajectories were again calculated using READY. It is clearly visible that pollutants entered Krakow from the north.   Fig. 13. Blueline again represents averaged PM 10 values in Krakow city but the red line shows averaged PM 10 values for the north sensors group outside the city. The situation is slightly different than presented in the example before. Here there are the following days on steadily decreasing temperature trend with a clear uptrend for pressure. We can observe continuous lag between sensors outside and inside Krakow. Of course, the lag for the maximum pick on 18 th March 01:00 for the north sensors group and sensors in Krakow is mostly dominated by the wind. The pollutants are transported to Krakow, but on the other hand in presence of north wind, they are quickly blown out from the city to the south. In the next days presented on this graph, the wind speed is very low, close to zero, so the higher concentration of PM 10 transported into the city remains there longer as the city is located in the valley. Fig. 19 shows also the 2 hours lag between distribution for the north group of sensors and sensors in Krakow. It seems that the terrain causes that pollution flowing in from the north takes longer to enter the city than when it enters the Vistula valley from the west. It is a valuable observation in the case of the future forecasting of the pollution level in Krakow city.

CONCLUSIONS
The conducted research clearly shows that pollutants generated in neighboring towns are transported with the wind to Krakow city. With a specific system of pressure, temperature and humidity, they can remain in the city to which they were transported for a long time. This situation can be even worst during the cold season when the Polish-type smog occurs (Wielgosiński and Czerwińska, 2020) Due to the partial lockdown introduced by the Polish government the PM concentration noise from transportation was limited and observation of the almost clear effect from solid fuels heating was possible. In addition, the analyses were carried out in temporal windows, in which car traffic was minimal. The temperature was also low enough and inhabitants of neighboring municipalities had to heat their houses. An important observation is that the west wind is conducive to the rapid transport of pollution to the city. Even if the wind speed is relatively low. Backward propagation study showed that pollutants emitted in the north can easily enter the city through the west air gate. The maximum PM10 concentration with the domination of these winds coincides with the Vistula River valley. The Vistula valley runs through important and historical parts of the city with increased tourist traffic, which may make Krakow's visitors feel that the city is a smog generator itself, while Krakow has one of the most pro-cleanair legislation in Poland in force. The lag between increased pollution in neighboring cities on the west and pollution increase in Krakow is about 1 hour. In the case of days when the north wind is dominant, the lag is about 2 hours. It is related probably to a natural barrier of hills on the north side. What is more, in presence of north wind, the pollutions are transported out much faster than it was when west winds occurred.
Banning the use of solid fuels for heating in selective cities does not relieve these cities from the air pollution problem related to solid fuels. It is important to extend the ban on solid fuel use for heating in Krakow to other localities in the Krakow agglomeration. Firstly, because of the health of the inhabitants of these particular towns, but also for the health of the inhabitants of Krakow. The research cited in the introduction clearly shows the facts of a health problems occurrence associated with exposure to air pollution. Secondly, because of the tourist traffic. After the transformation period, Krakow has become one of the most visited cities in Europe (Kowalczyk-Anioł et al., 2021), therefore taking care of the positive perception of the city, including clean air, is in the interest of the inhabitants of the region working in the tourism industry.