## 3 Results
### Kriging Results  
Ordinary kriging was compared against universal kriging with elevation drift to determine whether the latter, despite its higher computational demands, was necessary for our analysis. Comprehensive cross-validation experiments were conducted on 100 randomly selected timestamps from the study period. For all evaluation strategies, multiple error metrics were calculated, including Root Mean Square Error (RMSE), Mean Absolute Error(MAE), and their normalized counterparts (NRMSE and NMAE) using the interquartile range (IQR) normalization. The interquartile range, representing the difference between the 75 th and 25 th percentiles of the data, provides a robust measure of variability that is less sensitive to outliers than standard deviation. This validation approach enabled quantitative assessment of interpolation accuracy across diverse meteorological conditions and spatial configurations. The first evaluation strategy employed a nationwide comparison where a fraction of randomly selected weather stations (20%, equal to 96 sites) were used as reference points, with the remaining stations (80%, equal to 387 sites) serving as input data. The results of this approach, as presented in Table 4 and Figure 4, assessed the overall performance of both kriging methods across Poland's entire meteorological network, encompassing diverse topographical and climatic conditions. The second evaluation strategy focused specifically on mountainous counties, where topographical influences on meteorological variables are most pronounced, and therefore where differences between kriging methods are expected to be substantial, as presented in Figure 5. This targeted analysis used a fraction of stations (20%, equal to 10 sites) from six selected high-elevation counties (tartzanski, nowotarski, suski, zywiecki, limanowski, and myslenicki) as reference points, while maintaining input data from the rest of the stations in the region. This configuration tested the methods' ability to predict values in topographically complex terrain where elevation effects are most critical. The results, as presented in Table 5 and Figure 6, demonstrated that incorporating topographical influences through universal kriging provided substantial benefits, particularly in mountainous regions where elevation significantly affects meteorological variables. The comparison revealed notable differences between the two methods, with universal kriging capturing gradients with considerably greater precision in topographically complex terrain. These findings confirmed that elevation-informed interpolation represents spatial variations more realistically, justifying the use of universal kriging despite increased computational costs. The kriging implementation encountered several technical limitations that required careful handling to ensure robust interpolation results. Some attempts produced singularity errors, most commonly when estimating precipitation in low-variance conditions. This occurred primarily when all weather stations within the interpolation domain reported nearly identical values--a frequent scenario with precipitation readings. Our solution implemented a two-tiered approach to handle problematic interpolation scenarios. For cases of complete uniformity, where all values were exactly equal--occurring in approximately 8% of precipitation interpolation cases--the algorithm bypassed kriging computation entirely and directly assigned the uniform value to interpolation targets. For scenarios with minimal but detectable variation, which affected 1.2% of precipitation metric cases,