## 2 Materials and Methods
### Hydrothermal Coefficient  
For characterizing atmospheric moisture conditions, which are the basis for the drought phenomenon, the hydrothermal coefficient was selected, which combines both the parameters of air temperature and precipitation within a given period into the form of a synthetic index. The hydrothermal coefficient (HTC), developed by [PERSON] [36], is defined through the following equation:  
\[HTC\ =\ \frac{10\sum_{i=\ 1}^{n}P_{i}}{\sum_{i=\ 1}^{n}T_{i}} \tag{1}\]  
where  
\(n\)--length of the preceding period in days;  
\(P_{i}\)--precipitation amount on the \(i\)th day (mm);  
\(T_{i}\)--daily average of the air temperature on the \(i\)th day (\({}^{\circ}\)C). The HTC describes atmospheric drought if the accumulation of air temperature in the preceding period outperforms the accumulated precipitation during the period under consideration. Regarding the HTC values, very dry and dry conditions were assumed for HTC \(\leq\) 0.7 and 0.7 \(<\) HTC \(\leq\) 1.0, respectively [4]; similar thresholds were found for studies in Central Europe, applying the HTC for analyzing moisture conditions [37; 38]. HTC is included in the Handbook of Drought Indicator and Indices [39] as one of the indices useful for defining atmospheric drought. The accumulation period of precipitation and air temperature is usually assumed for drought assessment as multiples of ten days; such a principle was applied in the present work. As HTC is based on the current course of precipitation and air temperature, it reveals well the dynamics of changes in moisture conditions for crop areas. A time series for a given area can be created, which provides information on the water deficit in particular parts of the growing season. The differences in the course of the HTC between the years 2015 and 2017 are presented in Figure 3. These are more explicit than the differences in precipitation and air temperature for the same years (Figure 4), which proves that application of the HTC better explains the dynamics of changes of atmospheric moisture. The distribution of all empirical HTC values for an accumulation length equal to 30 days and spanning the years 2001-2019, calculated for the original data from the meteorological stations in all growing periods, is close to log-normal (Figure 5). The median was used as the average value estimator of this set of observations: It is approximately equal to 1.0. The distribution of HTC shows that the values around 1.0 are those that occurred most frequently and represent the average state of atmospheric moisture on the territory of Poland. Thus, HTC \(<\) 1 is assumed to indicate water deficit, while HTC \(>\) 1 indicates good moisture conditions. However, the spatial distribution of the HTC reveals various patterns; the local medians of the HTC comprise values significantly lower or higher than 1.0. In the case when the local median is lower than 1.0, rainfall deficit occurs more often within the corresponding area, and when it is higher than 1.0, good moisture conditions prevail within the area. Herein, such an approach was considered to characterize the climatic features of the area. The median of HTC calculated for the selected area informs about the average atmospheric conditions (in relation to precipitation and air temperature). To obtain the median HTC values for the entirety of Poland, a database of 1 km raster images of HTC was created using the daily interpolated temperature and precipitation from the meteorological stations in the period 2001-2019. These images refer to the growing season (from the end of April to September) and were formed with a 10 day step. The spatial distribution of HTC median values in Poland (Figure 6) is related to climatic conditions, which are influenced by Poland's topography (Figure 7).