## 4 Conclusions  
In this paper, we considered the impact of lightning data assimilation on the 3 h precipitation forecast over the central Mediterranean Sea. To achieve this goal, rapid update cycle (3 h) lightning data assimilation of the WRF model for the month of November 2019 was set up. This month was chosen because it was characterized by several precipitation events over Italy and the central Mediterranean area. A total of 232 three-hour-rainfall forecasts were considered for two different configurations of the WRF model, CTRL and LIGHT, the latter assimilating lightning data from the LINET network. To verify the model's performance, two different datasets were used: an IMERG gridded dataset at 0.1\({}^{\circ}\) horizontal resolution and six rain gauges in six Italian islands in the central Mediterranean Sea. LDA improves the precipitation forecast over the sea for the analyzed period. A comparison of the WRF forecast with the IMERG dataset clearly shows the positive impact of LDA, especially on the Ionian and Adriatic Seas. The anomaly correlation shows a good ability of WRF to predict rainfall both over land and sea, with few exceptions. LDA improves the forecast, especially for the first 20 days of the month, when convective events occurred more frequently compared to the last part of the month. The impact of LDA is larger over the sea than over land. This is confirmed by the analysis of the Taylor diagram. This diagram analysis, however, shows an underestimation of the precipitation standard deviation of the WRF model over the sea, which could be partially explained by a possible overestimation of the rainfall given by the IMERG dataset over the central Mediterranean Sea for the period selected in this paper. The comparison between the WRF forecast and the rainfall recorded over small islands reveals a positive impact of LDA for all cases except Ponza. Both the reduction in the false alarms and the increase in correct forecasts contribute to overall performance improvement. The case study of 12 November for the period 00-03 UTC shows how important LDA can be for specific cases. The CTRL forecast predicted the precipitation patterns a few tens of kilometers west of the real occurrence. This shift, however, has a notable impact on the precipitation forecast (double penalty error) because heavy precipitation is predicted over Calabria, where small amounts are recorded by rain gauges (false alarm), while the precipitation over the Ionian Sea is missed by the CTRL forecast (miss). Both errors are considerably reduced by LDA. While the aim of the paper is to show the impact of LDA over the sea, the forecast was also verified over land with the IMERG dataset. Results show a positive impact of LDA over the Italian peninsula, in agreement with the results already found by the same authors in past studies with WRF and RAMS@ISAC numerical weather prediction models [8; 30; 55]. The findings of this paper are of practical importance for two main reasons: First, the rainfall forecast over the sea is important for navigation, fishing, and many sea-related activities; second, over Italy, and more in general over the Mediterranean region, convection can be generated or can evolve over the sea and is then advected over land, causing, sometimes, high-impact weather. Having a better representation of the convection over the sea can help to improve the forecast of these events and better predict their effect over the coastal regions, which can be often devastating. While the results of this paper are encouraging, the seasonal variability of the Mediterranean climate requires further analysis to show the impact of LDA over the sea in different seasons. A dedicated study to evaluate the impact of LDA for convective events originating over the sea and advected over land is also necessary. These events are partially observed by radars, and LDA can contribute significantly to the improvement of precipitation forecast. It is important to note that this paper limits its analysis to LDA.