*4.2. Data Assimilation and Numerical Simulations*

Data assimilation was performed using a 3-Dimensional Variational (3D-Var) technique with the WRF Data Assimilation (WRFDA) system [50] in version 3.9.1. The 3D-Var scheme aims to improve initial conditions by minimizing a penalty or cost function that reduces the misfit between the background forecast and observations [51]. Several experiments that assimilated different datasets were carried out to assess the benefit of data assimilation for the nowcasting of severe convective events that can impact aviation operations. Radar reflectivity, temperature observations from in situ weather stations, and Global Navigation Satellite System (GNSS)-derived data were assimilated every 3 h within a 6 h assimilation window, whereas lightning data were assimilated every 15 min through

a nudging technique [52] that increased model instability by adding water vapor when flashes were observed. The results, widely discussed in [46], show that the assimilation of lightning data plays a key role in improving forecast skill. Indeed, the numerical experiment with radar and lightning data was able to produce reliable forecasts at high spatial and temporal resolution that are suitable for ATM purposes.
