## 2 Materials and Methods
### Proxies for the Deep Convection  
The main parameters used in the analysis and associated with each PF are reported in Table 1. GMI-based parameters are indicated in bold, while DPR-based parameter are indicated in italic. In the following, the main parameters used in the study, among those reported in Table 1, are described. The brightness temperatures (BTs) at 37 and 89 GHz are the most \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Parameter Description** \\ \hline ORBIT & Orbit number \\ YEAR & Year \\ MONTH & Month \\ DAY & Day \\ HOUR & Hour (UTC) \\ LAT & Geographical center latitude (degree) \\ LON & Geographical center longitude (degree) \\ NPIXELS & Number of radar pixels with precipitation \\ LANDOCEAN & 0: over ocean, 1: over land \\
**MIN85 PCT** & Minimum 89 GHz polarization corrected temperature (K) \\
**MIN37 PCT** & Minimum 37 GHz polarization corrected temperature (K) \\
**MIN1833** & Minimum 183.31 \(\pm\) 3 GHz BT (K) \\
**MIN1838** & Minimum 183.31 \(\pm\) 7 GHz BT (K) \\
**MIN165H** & Minimum 166 GHz H polarization BT (K) \\
**MIN165V** & Minimum 166 GHz V polarization BT (K) \\ _VOLRAIN\_KI_ & Volumetric precipitation from Ku (Km\({}^{2}\) mm/hr) \\ _MAXNSZ_ & Maximum near surface reflectivity (dBZ) \\ _MAXDBZ_ & Profile of maximum reflectivity (dBZ) \\ _MAXNSPECID_ & Maximum near surface precipitation rate (mm/hr) \\ _MAXHT_ & Maximum height of detectable radar echo (Km) \\ _MAXHT15_ & Maximum height with 15 dBZ echo (Km) \\ _MAXHT20_ & Maximum height with 20 dBZ echo (Km) \\ _MAXHT30_ & Maximum height with 30 dBZ echo (Km) \\ _MAXHT40_ & Maximum height with 40 dBZ echo (Km) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters associated with each PF in the V05 dataset. The first column reports the name of the parameter as it appears in the dataset, and the second column gives the description of each parameter referred to GMI and DPR Ku-band radar. In **bold** are the GMI-based parameters, and in _italic_ are the DPR-based parameters used in the study. important proxies of the intensity of a deep convective system [19]. Their minimum value for each PF can be associated with the strength of the updraft in the convective core [16] because the BT depression is mostly due to the scattering of the upwelling radiation by the ice hydrometeors. In particular, the 89 GHz channels provide information about the presence of precipitating high density ice in the convective core (sustained by the intense updraft), such as graupel or hail. The 37 GHz channels are mostly sensitive to the absorption/emission by liquid water (rainfall). However, in presence of intense convective cores, the scattering by high-density, large ice particles (graupel or hail) can cause significant BT depression at this (or even lower) frequency, thus enabling the detection of large hail (e.g., Reference [7; 38]). In Table 1, the Polarization Corrected Temperatures (PCTs) instead of BTs are used for 37 and 89 GHz channels. PCT has been introduced in previous studies to highlight the scattering signal of the cloud with respect to the signal associated with the radiatively cold background surface [39]. Cold BT signatures can result either from the low emissivity of sea or snow-covered surfaces, or from the scattering of ice particles within the clouds. The surface can contaminate the signal and BT response to the cloud in the low-medium frequency window channels (e.g., 37 and 89 GHz), and this effect is reduced with PCT defined in its general form as:  
\[PCT_{f}=\frac{\beta_{f}\cdot BT_{f_{b}}-BT_{f_{g}}}{\beta_{f}-1}, \tag{1}\]  
where \(BT_{f_{b}}\) and \(BT_{f_{g}}\) are, respectively, the horizontally and vertically polarized BTs at the frequency \(f\), while \(\beta_{f}\) is a parameter estimated in several studies for different frequencies [38; 39; 40]. The minimum PCT value at 37 GHz and 89 GHz associated with the PF (MIN37 PCT and MIN89 PCT in Table 1) are used as proxies for deep convection.