## 1 Introduction  
Public awareness of the air quality around the world is increasing. Many actions are being taken to increase environmental awareness. Local authorities around the world make decisions to reduce the levels of air particulate matter (APM). The environmental protection agencies prepared regulations according to the limit values of chemical substances in the atmosphere. The regulation is applicable to the European Union in accordance with the Directive 2008/50/EC [1]. However, in many cities, these limit values are still exceeded [1, 2, 3]. The influence of particulate matter on human health and the environment requires knowledge of the chemical content and size distribution of APM. Many studies have researched the characterization of particulate matter [4, 5, 6, 7]. Some of them also include the health effects of APM [8, 9]. APM can cause cardiovascular and respiratory diseasesand cancer. APM is associated with millions of premature deaths worldwide and with cardiovascular and respiratory diseases every year [10; 11; 12; 13]. Atmospheric PM varies in size and composition and consists of a mixture of primary pollutants (emitted directly from anthropogenic and natural sources) and secondary pollutants (formed in the atmosphere through reactions of primary pollutants) [14]. The chemical composition of particulate matter, as well as other characteristics of PM, can vary within wide limits in different areas, depending on the main emission sources, dispersion conditions, and chemical reactions that take place in the atmosphere, as well as the influence of the air masses transported from both neighboring and remote areas [14]. The contribution of sources is evaluated by different methods, such as receptor modelling. One such method is positive matrix factorization (PMF) [6; 7; 15; 16]. In some papers, SA methods have been described [16; 17; 18; 19; 20]. The main sources of PM determined by receptor modelling (108 European SA analysis) are the following: sea salt, soil, traffic exhaust, traffic non-exhaust, industry, secondary inorganic aerosols, solid fuel combustion (biomass burning and coal combustion) and other non-identified sources [15; 16]. A review of SA techniques conducted by [PERSON] et al. [21] identified 11 common PM source categories in 18 developing countries of Asia, Africa, and Latin America, grouped into four main types: (1) dust emissions, including road dust, soil dust, resuspension, fugitive dust, and construction; (2) transport (gasoline and diesel); (3) industrial activities, including coal and oil burning, brick kilns and power plants; as well as (4) nonurban, including biomass burning, long-range transport and marine sources. As a result, the chemistry, size distribution, or reactivity of PM vary widely from location to location and season to season, which induces large changes in health impacts depending on all of these parameters [22]. Krakow was one of the most polluted cities in Poland and Europe. Now, the situation is much better [23]; local authorities have taken many actions to reduce pollution in the city. In southern Poland, along the Vistula valley, the compact buildings and the location of Krakow in a concave form of land, isolated from the south by the mountain area, hinder the natural ventilation of the city via horizontal ventilation, i.e., the movement of pollutants by the emission wind from the place of emission to other areas [24; 25]. The main sources in Krakow are road traffic, solid fuel combustion, and industry. The Arcellor Mittal steel industry is located in the east part of the city. The power plants (PGE Energia Cieplna S.A. and CEZ Skawina S.A.) are in the east and southwest parts of the city, respectively. Source apportionment and chemical characterization have been carried out in Krakow since 2014 [26; 27; 28; 29]. PM\({}_{10}\) was characterized in the summer of 2018 and winter 2018/2019 at urban and traffic background stations in Krakow [30].