# Hailstorm Detection by Satellite Microwave Radiometers
## 3 The Hail Detection Model
### The MWCC Training Dataset
The result is that for \(TB_{184}^{var}\)\(<\) 25% the ice scattering mostly impacts on the category d \(<\) 10 cm but for bins with \(TB_{184}^{var}\)\(>\) 25% the average TBs largely diverge touching minimum values for d \(<\) 10 cm. The CO3 domain of two hailstorms is segmented in Figure 5 on the basis of \(TB_{184}^{cur}\) values. The first sequence of images (top) refers to the Colorado hailstorm (d \(<\) 3.5 cm) and shows the unfiltered patterns of CO3 (5a) and those filtered by 15% \(<TB_{184}^{var}\)\(<\) 25%, 25% \(<TB_{184}^{var}\)\(<\) 35%, and \(TB_{184}^{var}\)\(>\) 35% (Figure 5b,c,d respectively). As seen, only the first two \(TB_{184}^{var}\) classes capture hail signatures drawing the distribution of main hail cores leading different hail-size diameters. Consistent with the relatively small hail diameters, no hail signals for \(TB_{184}^{var}\)\(>\) 35% have been found. The second series of images displays the event over South Dakota (Vivian) where the measured hail size at the ground was around 11 cm. In this case, the sequencing of the whole dataset (Figure 5e) with the \(TB_{184}^{var}\) thresholds demonstrate as the smaller ice particles (low scattering) are collected by 15% \(<TB_{184}^{var}\)\(<\) 25%, (Figure 5f) but the signal associated with hail is sampled by classes \(TB_{184}^{var}\)\(>\) 25% (Figure 5g,h). In particular, \(TB_{184}^{var}\)\(>\) 35% (Figure 5h) caught the highest TB reductions correlated to the extinction by very large hail. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**TB90 (K)** & **TB150 (K)** & **TB184 (K)** & **TB186 (K)** & **TB190 (K)** & \(TB_{184}^{var}\) (\%) (2 \textless{} d \textless{} 10\))** & **No. of Data** \\ \hline
241.79 & 204.37 & 209.07 & 199.57 & 194.15 & 15–25 & 94 \\
218.65 & 182.31 & 212.54 & 196.51 & 182.63 & 25–35 & 295 \\
197.00 & 160.60 & 201.18 & 180.17 & 163.76 & \(>\)35 & 54 \\ \hline
**TB90 (K)** & **TB150 (K)** & **TB184 (K)** & **TB186 (K)** & **TB190 (K)** & \(TB_{184}^{var}\) (\%) (d \textgreater{} 10\))** & **No. of Data** \\ \hline
250.34 & 217.48 & 206.64 & 205.36 & 195.85 & 15–25 & 416 \\
220.66 & 181.58 & 200.28 & 189.55 & 175.11 & 25–35 & 233 \\
174.90 & 148.91 & 175.24 & 161.43 & 147.37 & \(>\) 35 & 91 \\ \hline \end{tabular}
\end{table} 
Table 3: Averaged brightness temperatures as function of \(TB_{184}^{var}\) for different hail diameters (d). Figure 5: _Cont._  
The investigation on the individual channels reveals the high capabilities of the MHS frequencies in detecting the variations of cloud ice bulk and estimating the hydrometeor properties during deep convection. Nevertheless, not all channels contribute at the same level of significance. Frequencies at 90, 150, and 190 GHz perform better in describing the ice scattering regime of convective cores containing hail and this makes them primary candidates as proxies for hailstorm detection. A closer examination of the previous results adds some further considerations. First, low perturbations induced by relatively low scattering as described by \(TB_{184}^{var}\) \(<\) 25% are very difficult to be directly associated with hail signatures. Hence, CO3 cloud features belonging to this class cannot be directly related to hail clouds. Second, moderate to high TB reductions observed for 25% \(<TB_{184}^{var}\) \(<\) 35% can be associated to hail but only the 150 and 190 GHz channels revealed high sensitivity to hail size modifications. This is probably due to the sensitivity of these wavelengths to the minimal variations of ice size distribution while the dynamic range at 90 GHz typically senses scattering by large to very large hail as observed by the \(TB_{184}^{var}\)\(>\) 35% class. The threshold \(TB_{184}^{var}\)\(>\) 25% is then applied to the whole dataset in order to isolate the TB values useful to calibrate the hail detection model. In summary, we explore the combinations of the most sensitive MHS channels to evaluate the best frequency differences fitting hail signatures.