## 3 Available Data  
For this study, a measurement campaign lasting from June 2020 to May 2021 and consisting of 400 six-week field measurements in 50 different geographical locations around Slovakia (see Figure 1) provided the values of three target variables that together characterize the local environmental pollution levels (see Appendix A):  
S--total pollution deposit  
Sr--soluble fraction of pollution deposit  
g02--electrical conductivity of soluble fraction  
The campaign produced eight six-week measurements per variable per location. The established procedure as per STN 33 0405 mandates fitting a Weibull distribution to the eight values of each variable obtained at each location, and then estimating its upper bound as the 99.5-th percentile of the fitted distribution. It means that, in a given location, there is only a 0.5% chance that the variable will exceed its local upper bound. Based on these three local upper bounds (for S, Sr, and g02), each location is assigned to one of four grades of environmental pollution (I-IV) and, for each grade, appropriate parameters of insulation and maintenance procedures are prescribed. We also had access to standard atmospheric pollution indicators regularly monitored and evaluated by the Slovak Hydrometeorological Institute (SHMU) [14], which consist of the yearly average of atmospheric concentrations of dust particles and selected gasses over Slovakia. These are the same attributes that we had used in our previous work [15], and we refer to them here as the SHMU input attributes. They comprise:  
* PM2.5--yearly average of concentrations of dust particles with a diameter less than 2.5 \(\mu\)m;
* PM10--yearly average of concentrations of dust particles with a diameter less than 10 \(\mu\)m;
* O\({}_{3}\)--yearly average of ozone concentrations;
* NO\({}_{2}\)--yearly average of nitrogen dioxide concentrations;
* SO\({}_{2}\)--yearly average of sulfur dioxide concentrations. In our previous work [15], we carried out several experiments in an attempt to reliably estimate the upper bounds of target variables S, Sr, and g02 on the basis of SHMU input attributes, but we failed to achieve reliable estimates. Neither nonlinear transformations of these attributes, nor their joint combinations, resulted in a substantial increase in the accuracy of our models. Possible reasons for this failure include:  
* An insufficient number of data records (i.e., insufficiently representative data set), which does not allow for generalizing the relationship between the inputs and the outputs;
* Missing input variables with dominant effect on target attributes, which makes the behavior of target variables appear to be random;
* Unknown confidence intervals for input and output attributes that reduced the accuracy of the used models;
* An insufficient spatial density of the measured input and output values;
* An inherent difficulty of learning to reliably estimate upper bounds of random variables. Overall, this seemed to indicate that the problem was much more difficult than it originally appeared, and a fundamental change in approach along with new relevant input attributes would be necessary to tackle it successfully. Therefore, this study exploits new input attributes primarily derived from satellite imagery. Figure 1: Locations of field measurements in our 2020–2021 campaign around Slovakia. The collection of Sentinel-2 satellite images used for this purpose aligned with the timing of our field measurements. Each image covered an area of 100 km \(\times\) 100 km and its maximum spatial resolution was 10 m per pixel. (Spatial resolution actually depends on the sampled spectral band--see Table 1). Since the lift-off of the second Sentinel-2B satellite in 2017, temporal resolution of these images is one image per five days [17]. These images can be either Level 1 (capturing the top of atmosphere reflectances) or Level 2 (bottom of atmosphere reflectances).