# Hailstorm Detection by Satellite Microwave Radiometers
## 3 The Hail Detection Model
### The MWCC Training Dataset  
Two independent datasets were used to quantify hail signals and calculate the statistics of the hail detection method. The first, where MHS data are used to directly estimate the impact of hail on TBs, is extracted from the hailstorms listed in Table 1. Each event is binned in the two classes of diameters of Table 2 and then the average TB reduction is calculated. The second dataset is derived from the 10-year (2000-2009) MHS measurements co-located with hail reports over the US. This matchup dataset already used to develop the prototype algorithm in [29] was derived from satellite overpasses within 5 min and 25 km distance from hailstorm locations, and restricted to an AMSU-B local zenith angle of 25\({}^{\circ}\) in order to reduce the impact of changing FOV size due to the scanning geometry. As discussed in Section 2.1, a preliminary classification of clouds through the MWCC is needed for mapping those convective clouds where hail signature can be recognized. Because the interest is in severe storms, only deep convections classified as CO3 have been isolated and assumed to be associated with hail. Let us consider that in this domain only limited areas of the cloud can be related with hail. Thus, when hail is captured the signal is much higher than that of the background no-hail areas, showing a very strong TB depression. In order to better discriminate all signals associated with hail, the TB variation at 184 GHz \(TB^{\text{sur}}_{184}\) (see Equation (1)) as distributed in the CO3 category has been analyzed. Therefore, three sensitivity classes based on the \(TB^{\text{sur}}_{184}\) values have been defined on the basis of the simple concept that \(TB^{\text{sur}}_{184}\) tends to increase by increasing the amount of growing ice, which is in turn related to the vertical development of convection. The magnitude of \(TB^{\text{sur}}_{184}\) is then related to the convection depth: high values of \(TB^{\text{sur}}_{184}\)mean high convection severity (high scattering) and then high probability of hail. Table 3 shows the average TBs for each \(TB_{184}^{cur}\) bin. As demonstrated by [PERSON] (2016), the TB magnitude tends to decrease with hail diameter and the impact of hail size is modulated by the observing frequency: high frequencies sense the scattering from a wide range of hail diameters while lower frequencies miss the majority of the scattering signal from smaller ice particles and their use is usually limited to very large hailstones. Table 3 shows that the average TBs decrease with increasing hail diameters and \(TB_{184}^{cur}\) values. Generally, high \(TB_{184}^{cur}\) values correspond to low TBs reaching the minimum values for d \(>\) 10 cm. A detailed analysis demonstrates that when \(TB_{184}^{var}\) \(<\) 25% the TBs show no noticeable reduction from d lower to higher than 10 cm. However, a comparison between the two first rows of Table 3 highlights that averaged TBs are apparently higher for d \(>\) 10 cm with respect to those associated with smaller d. This result appears physically contradictory, but can be justified by considering that in this class the TB variability is due to several factors linked to the intrinsic dynamics of each class. Hailstorms belonging to the class d \(<\) 10 cm are generally characterized by a large variety of ice aggregates coexisting on top of convection towers. This large particle size distribution, when segmented by \(TB_{184}^{var}\) values, tends to fill the first two bins with a tendency to aggregate in the first bin where the median diameter value (4.5 cm) belongs. On the contrary, hailstorms where d \(>\) 10 cm are often characterized by hail cores clustered in a restricted area of convective clouds. Then large hail distributes in the bins where \(TB_{184}^{var}\)\(>\) 25% leaving very small frozen hydrometeors (possibly associated with supercooled water) in the first bin where \(TB_{184}^{var}\)\(<\) 25%.