## 1 Introduction  
The Mediterranean Sea is one of the most interesting areas of the world for what concerns extreme weather phenomena, and it is considered as one of the most cyclogenic basins [1], and as one of the main climate hot-spots [2]. During the year, several heavy precipitation systems develop over the sea, hitting the densely populated coastal areas, causing severe damages and sometimes casualties. Several typologies of intense Mediterranean weather systems are reported in literature. The most common and dangerous, and often difficult to predict, are those associated with deep convection, i.e., characterized by strong updrafts, extending vertically to the troposphere and, sometimes, penetrating through it in the most intense cases (overshooting tops, e.g., Reference [3]). Severe deep convection is often responsible for most weather-related natural disasters, such as floods, landslides, intense damaging hailistorms, or tornadoes. Other than the classic intense isolated thunderstorms, the Mediterranean area has other severe thunderstorm typologies. Enhanced V-shape systems, so-called because of the characteristic V-shape observed from VIS/IR satellite images due to deep convection interference with upper level flow (e.g., Reference [4]), are the most common intense types of thunderstorms. They often originate from the low-level convergence of winds along the line separating the cold air mass on the eastern edge of the ascending branch of a deep trough from the warm air of the anticyclone. These events are associated with regenerating thunderstorms, and are capable of producing a large amount of precipitation within few hours, together with high lightning flash rates, remaining stationary over the same affected areas (e.g., the Livorno flash flood in September 2017, described in Reference [5]). Although less common than in other parts of the world, several cases of thunderstorms with supercellular characteristics are also reported in the Mediterranean area [6; 7; 8; 9]. The vast majority of reports of supercells is associated with large hail, with diameters greater than 5 cm, torrential rainfall, extremely high lightning flash rates, and strong wind gusts, sometimes associated with tornadoes [10]. For this reason, extreme damages to infrastructures, and fatalities are reported when supercells hit the coast. On 28 November 2012, for example, a multivortex tornado belonging to the third class of the Enhanced Fujita Scale (EF3, maximum wind speed of approximately 230 km h\({}^{-1}\)), associated with an intense supercell, hit the Apulia region, in Southern Italy, focusing over the city of Taranto [9] and causing one casualty and extensive damages. Sometimes, Mesoscale Convective Systems (MCS), i.e., clusters of several thunderstorms organizing at the mesoscale and creating structures with multiple cells in different stages of development, can be found in the Mediterranean area. This happens under specific ideal conditions for their development, in particular during a cold front outbreak or with the presence of a cut-off low [11]. These structures are associated with heavy rainfall and flooding events [5] because of their well-organized long-lasting activity due to the continuous replacement of old cells into young cells inside the MCS structure [11]. One of the main challenges associated with deep convective systems, especially when rapidly evolving and extremely localized, is their prediction using Numerical Weather Prediction (NWP) models. Moreover, it is becoming very important to understand their intensification and feedback mechanisms, especially in a climatic hot spot, such as the Mediterranean region, through a synergistic use of models and observations. It is, therefore, fundamental to increase the knowledge of these events, and to study their microphysical properties, even in areas not covered by ground-based instruments (e.g., weather radars).