## 1 Introduction
[38] for eight events over Greece, showing improvement of the precipitation forecast given by LDA up to 24 h.  
[PERSON] et al. [29] were the first to consider LDA in a convection resolving model (the weather research and forecasting (WRF) model at a 3 km horizontal resolution) using a methodology that imposed incremental increases in water vapor mass in the mixed-phase region (0 \({}^{\circ}\)C-20 \({}^{\circ}\)C layer) based on observed lightning flash density rates and simulated graupel mixing ratio. This same nudging method was applied for over 70 days during the 2013 warm season over the contiguous United States, showing the important and positive impact of LDA for a prolonged forecast period [39]. [PERSON] et al. [40] improved the forecast of a derecho event up to 6 h with LDA and showed that LDA can be comparable to that of three-dimensional variational assimilation (3 DVAR) of radar data (radial winds and reflectivity factor). [PERSON] et al. [41] adapted the nudging function of [PERSON] et al. [29] to adjust graupel, snow, and ice crystal mixing ratios and applied it to a quasi-linear convective system over northern China, showing that the assimilation of graupel, snow, and ice crystals is important for outflow-dominated events. [PERSON] et al. [42] proposed a data assimilation scheme, based on the functions of [PERSON] et al. [29] and [PERSON] et al. [41], which takes into account the dynamical and thermodynamic conditions. [PERSON] et al. [8] implemented the method of [PERSON] et al. [29] in the regional atmospheric modeling system (RAMS) model and obtained a substantial improvement of the quantitative precipitation forecast (QPF) for 20 cases over Italy that occurred during Hydrological Mediterranean Experiment-Special Observing Period 1 (HyMeX-SOP1) [43]. Recently, [PERSON] et al. [30], using the WRF model, applied the method of [PERSON] et al. [29] to evaluate the impact of LDA for three case studies of severe weather that occurred over Italy. The three cases span a range of convective precipitation from a long-lived, wide-area intense-precipitation event to a heavy and localized rainfall case. WRF was used in an RUC data assimilation system (3 h and 6 h forecast). The LDA improved the quantitative precipitation forecast in all cases and for both temporal ranges. The Mediterranean area is prone to heavy precipitation, and floods and flash floods are the most common and dangerous natural hazard in the area [44]. Several research studies have been carried out to explore these events in the Mediterranean. The HyMeX project [43; 45] and previously the MEDEX (The Mediterranean Experiment) project [46] considered the water cycle in the Mediterranean basin, and the study of floods and flash floods were among the main topics of both projects. Heavy-rainfall events over the Mediterranean occur mainly in fall and winter and have been reported in numerous papers ([44; 47; 48; 49; 50; 51; 52; 53; 54; 55], among many others). The role of the Mediterranean Sea in heavy-precipitation storms has been also considered in the literature [56; 57; 58; 59]. Because the Mediterranean Sea is a warm sea, it feeds the cyclones with large amounts of water vapor, reinforcing the cyclones and increasing their lifetime [60]. Often, storms form over the Mediterranean Sea [61; 62; 63], or spend most of their lifetime over the sea, as in the case of Medicanes [64; 65; 66], and are then advected toward land, causing floods, windstorm, and surges. For these cases, the air-sea interaction plays a major role in the storm evolution. A better high-impact weather forecast over the sea would result in a more realistic simulation of its impact once it hits the coast and would be of practical importance for many sea-related activities (fishery, navigation, tourism, etc.).