## 3 Results  
### Categorization of PFs with Deep Convection Proxies: Diurnal and Seasonal Distribution  
The convective proxies reported in Table 1 are divided taking the top 0.01, 0.1, 1, and 10% values of the distributions. The intensity classes obtained are identified as reported in Table 2. In Figure 3a,b, the geographical distributions of PFs' intensity classes of MIN37 PCT and MAXHT40 parameters, respectively, are reported, with the extremes of each range indicated in the colorbar. It is worth mentioning the presence of several extreme precipitating systems with a MIN37 PCT below 162 K (0.01% coldest values, class 1) and some MAXHT40 values reaching and exceeding 9.88 km (0.1% highest values, class 1 and class 2), indicating intense vertical updraft and suspended high-density large ice particles within the convective core. It is interesting to note how, especially in Figure 3b, there is a tendency for precipitating events with strong convective signatures to occur more over land than over sea, similarly to what observed in the tropics and subtropics [19; 26]. However, several PFs belonging to the top 0.01% classes of the two parameters (black dots) are found over sea. It is worth noting that the extreme PFs found with the two criteria do not always coincide. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Class** & **Interval of Values** & **Color** \\ \hline
1 & top intense 0.01\% values & black \\
2 & top intense 0.1\% values not belonging to the top intense 0.01\% & red \\
3 & top intense 1\% values not belonging to the top intense 0.1\% & blue \\
4 & top intense 10\% values not belonging to the top intense 1\% & green \\
5 & values not belonging to the top intense 10\% & grey \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Intensity classes defined for each parameter distribution. The colors used to identify each class in Figure 3a,b are also listed. Figure 3: Location and intensity categories of deep convection PFs identified according to the minimum PCT at 37 GHz (MINPCT37) **(a)** and to the 40 dBZ echo maximum height (MAXHT40) (**b**). For each category, the range of MINPCT37 and MAXHT40 values and the corresponding top percentages are reported in the colorbars. Figure 4a-d show the distributions of these PFs in summer (June-July-August, JJA) and winter (December-January-February, DJF) on a 2\({}^{\circ}\)\(\times\) 2\({}^{\circ}\) grid. In each panel, the top 3 intensity classes of the MIN37 PCT or MAXHT40 proxies are considered (i.e., all PFs with the top 1% values for each selected proxy for the whole four year period). The colors represent the number of PFs in each grid box for the four-year period. Differences in the geographical distribution of the most intense PFs within the domain are observed between seasons, in accordance with the seasonal large scale circulation that characterizes the Mediterranean region. More densely populated grid boxes are found during the summer over northern Italy and generally over the Balkan Peninsula and in the areas between northern Spain and southern France. This confirms how the mechanism of deep convection is mainly driven by radiative heating, stronger during the summer season, and by the complex orography in this areas. During the winter, the number of PFs per grid box with the maximum 40 dBZ radar echo top heights >6 km does not exceed 4 (Figure 4d), due to the low energy available for precipitation systems, and because it is quite rare to find the conditions to have strong updrafts, except in few cases of synoptic origins where convection is forced by extra-tropical cyclones. The number of PFs within each grid box is different when different proxies are considered, since different subsets of elements are selected from the entire dataset. However, the main result is the similarity in the geographical distributions obtained with DPR-based and GMI-based criteria for each considered season.