## 2 Materials and Methods
### Meteorological Data Interpolation  
Historical weather data are available solely at the locations of meteorological stations, whose network is both unevenly distributed across the country and sparse, particularly in relation to the localized county-level context of the dataset (Figure 1). This uneven distribution of meteorological stations creates challenges in directly linking weather conditions to specific accident locations, especially in areas where stations are distant or lacking. The data gaps posed by the spatial limitations of this network could lead to inaccurate or incomplete weather information for certain regions.  
Before performing the analysis, we split the meteorological stations into two categories: those that exclusively record precipitation data and those that, in addition to precipitation, offer temperature and humidity measurements. The number of stations collecting precipitation data is more than twice that of stations providing the additional meteorological parameters. While this higher station density improves spatial coverage for precipitation measurements, accurately estimating precipitation conditions remains particularly challenging due to its variability and highly localized nature [25]. Unlike temperature and humidity, which exhibit smoother spatial patterns, precipitation can be influenced by small-scale atmospheric processes, making interpolation and extrapolation more complex.  
We used a histogram to examine the distance between each incident location and the nearest meteorological station from the IMGW network that was operational at the time of the incident, calculated based on their geographic coordinates (Figure 2). The results reveal that the majority of accidents occurred within 12 km of a station providing precipitation measurements and within 16 km of a station recording temperature and humidity data. These proximities suggest that, for a significant portion of cases, the available meteorological observations offer a reasonable approximation of local weather conditions. However, a substantial number of accidents were recorded at much greater distances--exceeding 40 km for precipitation data and 60 km for temperature and humidity measurements. This spatial disparity, especially for precipitation, increases the likelihood of notable inaccuracies in the estimated weather conditions at accident sites.  
To address the challenge of accurately estimating weather conditions, we employed kriging to interpolate temperature, humidity, and precipitation across Poland. Kriging is a geostatistical interpolation method that provides the best linear unbiased predictions for unsampled locations by leveraging the spatial autocorrelation present in observed data. Its strength lies in effectively incorporating spatial dependencies among observations, making it particularly suitable for modeling continuously varying phenomena like temperature.  
Utilizing the geolocation data of weather stations provided by IMGW, we were able to generate a continuous data surface from discrete measurements. By incorporating data from multiple stations, kriging reduces the impact of large observation gaps, particularly for precipitation, where localized variability can be significant. To enhance interpolation accuracy, we incorporated elevation data as a drift term in the kriging process, which proved especially valuable for mountainous regions where topography significantly influences weather patterns. This approach allowed us to overcome the limitations of station density variability, ensuring that even regions with sparse observational coverage were accurately represented.  
Together, the interpolated data provided a comprehensive representation of weather conditions across Poland at any given time, enabling a detailed analysis of how varying meteorological factors influence road traffic incidents.