## 1 Introduction  
Precipitation is one of the key elements of the hydrological, cycle and it is an important phenomenon that affects human lives. It is then critical to provide precipitation forecast for different time horizons. A short-range precipitation forecast is fundamental for flood forecasting, early warning, and hydrological applications [1; 2; 3; 4]. Numerical weather prediction (NWP) models use the physical descriptions of the many atmospheric processes and have been used for the short-term forecast of precipitation [5; 6; 7; 8]. NWP models have improved significantly in recent years both in their physical parameterizations and in their spatial resolutions, thanks to the continuous advancement of the knowledge and of the computational resources [9; 10; 11]. Despite the continuous improvement of NWP, the accurate prediction of high-impact weather is one of the challenges of state-of-the-art numerical weather prediction (NWP) models [12; 13; 14]. The NWP models for short-range forecasting purposes require more observational data and effective assimilation methods to overcome the spin-up problems [10; 11]. Thanks to the ever-increasing computing power and to the possibility of assimilating different types of observations, the forecast of severe weather events has improved constantly in the past decades [15; 16]. Lightning data have been widely used in the past two decades and have some advantages compared to other sources of data [17; 18]. For example, an important source of data to improve effectively the precipitation forecast at short range is given by radars (reflectivity and radial winds) [19; 20; 21; 22]. However, compared to lightning data assimilation (LDA), the assimilation of radar data is achieved through more sophisticated and computationally expensive techniques, such as three-dimensional variational assimilation (3 DVAR) [23; 24] and the ensemble Kalman filter [20; 25; 26]. Flashes are observed with a sub-kilometric position error (this error is less than the spatial horizontal resolution of the meteorological model used in this paper, i.e., 3 km) and time (the detection of the strokes is instantaneous and much lower than the time step used in meteorological models). Since lightning is associated with convective activity, a positioning of the lightning in space and time gives a positioning of the most intense convective areas in meteorological systems [27; 28]. Lightning data are simple to transfer and do not require a wide-band network connection. The process of computing the lightning position from the electromagnetic signals detected by sensors is fast, making lightning observations available in real time. For the above reasons, LDA is suitable for improving the forecast of intense convective weather events in rapid update cycle (RUC) data assimilation systems. Broadly speaking, LDA can be divided into two classes: LDA in models parameterizing convection (horizontal resolution > 3-5 km) and LDA in models explicitly resolving the convection (horizontal resolution < 3-5 km) [18; 29; 30]. The first attempts to assimilate lightning in NWP models were based on relationships between lightning and the rainfall rate estimated by microwave sensors on board polar-orbiting satellites [31; 32; 33; 34]. These studies demonstrated not only the ability of LDA to improve the precipitation forecast but also the improvement of large-scale field forecasts, such as sea-level pressure. [PERSON] et al. [35] used rain rates as a proxy for lightning and implemented LDA in an RUC data assimilation system. [PERSON] et al. [36] used lightning to locate convection, and the simulated water vapor profile was nudged toward vertical profiles recorded during convective events. [PERSON] et al. [17] used lightning data to control the triggering function within the Kain-Fritch cumulus scheme [37] as a function of the flash rate. This method can also suppress the activation of the cumulus parameterization scheme whenever the model simulates unobserved lightning. The same method was also applied by [PERSON] et al.