## 2 Materials and Methods
### Proxies for the Deep Convection
In addition, the minimum BTs at 166.5 GHz (V and H polarization), 183 \(\pm\) 3 GHz, and 183 \(\pm\) 7 GHz (indicated as MIN165V, MIN165H, MIN1833, MIN1838 in Table 1) are also used in the analysis as additional proxies for the categorization of intense PFs, since they are sensitive also to the scattering of smaller ice particles found in the upper layers of the clouds (including the anvil). Some radar-based proxies, in Table 1, are the maximum heights reached by specific radar echoes. For example, MAXHT20 and MAXHT40 indicate the maximum radar echo height at 20 dBZ and 40 dBZ, respectively. These give information about the updraft strength of a storm and its convective nature since the deeper the convection, the more vertically developed the precipitation structure and, therefore, the higher the maximum height of a given radar echo [19]. Figure 1: Maps (in \({}^{\circ}\)N Latitude and \({}^{\circ}\)E Longitude coordinates) of Polarization Corrected Temperature (PCT) at 37 GHz (**a**) and 89 GHz (**b**), and Brightness Temperature (BT) at 166 GHz (V polarization) (**c**) for the MCS of 20 September 2014 over the Adriatic Sea. The black line indicates the position of the vertical cross-section shown in Figure 2. The colorbar refers to the PCT and BT values. An example of the effectiveness of PCTs to identify convection over land and sea is provided for an intense MCS, that hit Emilia-Romagna region (Italy), causing extensive and intense rainfall and floods in several river basins and then moved to the Adriatic Sea and the coasts of Croatia, between 14 and 20 September 2014. Figure 1a-c show the maps of the 37 GHz PCT, the 89 GHz PCT, both obtained from Equation (1), and the BT at 166 GHz (V polarization), respectively, for the GMI overpass on 20 September 2014 over the Adriatic Sea. The most intense region of the storm interested by deep convection are well highlighted by the marked PCT depressions compared to the warm background in Figure 1a,b, while the radiatively cold sea surface that would be visible in the BT images, is not contaminating the scene. In particular, the low values reached in the convective core confirm the extremely intense nature of the system, with minimum values of PCT at 37 GHz and 89 GHz of 135 K and 68 K, respectively. These values are comparable to the values reported by [PERSON] et al. [7] for an extremely intense hailstorm occurred near Naples, Italy, on 5 September 2015, and are compatible with the presence of large and high density precipitating ice particles (hail) and strong updrafts. On the other hand, 166 GHz (V pol) BT shows the large extension of the system, including the anvil, with an extended area of cold brightness temperatures compared to the warm background, due to scattering from ice particles in the stratiform region, and lower values in correspondence to the convective cores (Figure 1c). The strength of the convection is also well depicted by a vertical cross section of DPR Ku-band measured reflectivity (reported in Figure 2 in correspondence of the black lines of Figure 1a-c). In addition, the BTs measured by GMI within the considered scan line are also reported. The strength of the updraft is confirmed by the maximum height of the minimum detectable radar echo (labeled as MAXHT in Table 1) above 16 km, as well as by the maximum height at 20 dBZ and 40 dBZ (reported in Table 1 as MAXHT20 and MAXHT40), around 15/16 km and 13/14 km, respectively. These variables are, indeed,  
Figure 2: Vertical section (position is indicated in Figure 1a–c) of DPR cross-track Ku-band measured reflectivity and GMI brightness temperatures along the section (colored solid and dashed curves) for the MCS of 20 September 2014 over the Adriatic Sea. The colorbar refers to the measured reflectivity values (in dBZ), while the right-hand side y-axis reports the brightness temperature values (in K). The legend refers to the GMI channels shown in the figure.